Quantrex Academy Quantrex AcademyPYQs with solutions · JEE · NEET · NDA

Home · JEE PYQs · Mathematics · Differential Equations

JEE Differential Equations PYQs with Solutions

586 previous year questions from Differential Equations (JEE Main & Advanced Mathematics) with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

586 questionsMathematics2007–2026Answers + solutions

About Differential Equations PYQs

Differential Equations has 586 previous year questions in the Quantrex Academy JEE Main & Advanced Mathematics bank. The 220 questions in this list come from JEE Main (191) and JEE Advanced (29), spanning 2007 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

Questions by year (this list)

  • 2026: 22
  • 2025: 24
  • 2024: 33
  • 2023: 27
  • 2022: 40
  • 2021: 43
  • 2020: 12
  • 2019: 1
  • 2018: 3
  • 2017: 2
  • 2016: 2
  • 2015: 2

Differential Equations questions with solutions

1

Let y : (-∞, ∞) arrow (0, ∞) be the solution of the differential equation (dy)/(dx) = e^ 5x y^3 + y^3 e^x + e^x y^4 , satisfying y(0) = 1 2 . Then the value of y( _e 2) is

JEE Advanced 2026 Solution View → 2

Let y = f(x) be the real valued function defined on the interval (0, ∞) , satisfying y(1) = 0 and the differential equation x(dy)/(dx) = y - x^3 . Then which of the following

JEE Advanced 2026 Solution View → 3

Let y=y(x) be the solution of the differential equation x 1-x^2 \,dy + (y 1-x^2 - x ^ -1 x)dx = 0 , x ∈ (0, 1) , _ x→ 1^- y(x) = 1 . Then y((1)/(2)) equals:

JEE Main 2026 Solution View → 4

Let y = y(x) be the solution of the differential equation (x^2 - x x^2 - 1 )dy + (y(x - x^2 - 1 ) - x)dx = 0 , x ≥ 1 . If y(1) = 1 , then the greatest integer less than y( 5 ) is

JEE Main 2026 Solution View → 5

Let y = y(x) be the solution of the differential equation ( x)^ 1/2 \,dy = ( ^3 x - ( x)^ 3/2 y)\,dx , 0 < x < (π)/(2) , y((π)/(4)) = 6 2 5 . If y((π)/(3)) = (4)/(5)α , then α^4

JEE Main 2026 Solution View → 6

Let y = y(x) be the solution of the differential equation x ((y)/(x))dy = (y ((y)/(x)) - x)dx , y(1) = (π)/(2) and let α = ( y(e^ 12 ) e^ 12 ) . Then the number of integral values

JEE Main 2026 Solution View → 7

Let y=y(x) be the solution of the differential equation: (dy)/(dx)+( 6x^2+(3x^2+2x^3+4)e^ -2x (x^3+2)(2+e^ -2x ) )y=2+e^ -2x , x ∈ (-1,2) , satisfying y(0)=(3)/(2) . If

JEE Main 2026 Solution View → 8

Let y = y(x) be the solution of the differential equation (dy)/(dx) = (1 + x + x^2)(1 - y + y^2) , y(0) = (1)/(2) . Then (2y(1) - 1) is equal to:

JEE Main 2026 Solution View → 9

Let x = x(y) be the solution of the differential equation 2y^2 (dx)/(dy) - 2xy + x^2 = 0 , y > 1 , x(e) = e . Then x(e^2) is equal to:

JEE Main 2026 Solution View → 10

If the curve y = f(x) passes through the point (1, e) and satisfies the differential equation dy = y(2 + _e x)\,dx , x > 0 , then f(e) is equal to :

JEE Main 2026 Solution View → 11

Let y = y(x) be the solution curve of the differential equation (1 + x)(dy)/(dx) + (y+1) x = 0 , y(0) = 0 . If the curve y = y(x) passes through the point (α, (-1)/(2)) , then a

JEE Main 2026 Solution View → 12

Let y=y(x) be the solution of the differential equation x ~d y ~d x -y=x^ 2 x, x ∈(0, π) . If y((π)/(2))=(π)/(2) , then 6 y((π)/(6))-8 y((π)/(4)) is equal to :

JEE Main 2026 Solution View → 13

Let y=y(x) be the solution of the differential equation x (d y)/(d x)- 2 y=x^ 3 (2-x^ 3 ) ^ 2 y, x ≠ 0 . If y(2)=0 , then (y(1)) is equal to

JEE Main 2026 Solution View → 14

Let y=y(x) be a differentiable function in the interval (0, ∞) such that y(1)=2 , and _ t arrow x ( t^ 2 y(x)-x^ 2 y(t) x-t )=3 for each x>0 . Then 2 y(2) is equal to

JEE Main 2026 Solution View → 15

If the solution curve y=f(x) of the differential equation (x^ 2 -4) y^ -2 x y+2 x(4-x^ 2 )^ 2 =0, x>2 , passes through the point (3,15) , then the local maximum value of f is

JEE Main 2026 Solution View → 16

Let y=y(x) be the solution of the differential equation x^ 4 ~d y+(4 x^ 3 y+2 x) d x=0, x>0, y((π)/(2))=0 . Then π^ 4 y((π)/(3)) is equal to :

JEE Main 2026 Solution View → 17

Let f be a twice differentiable non-negative function such that (f(x))^ 2 =25+∫_ 0 ^ x ((f(t))^ 2 +(f^ (t))^ 2 ) dt . Then the mean of f( _ e (1)), f( _ e (2)), ….., f( _ e (625))

JEE Main 2026 Solution View → 18

If y=y(x) satisfies the differential equation 16( x+9 x )(4+ 9+ x ) y ~d y=(1+2 y) d x, x>0 and y(256)=(π)/(2), y(49)=α , then 2 α is equal to :

JEE Main 2026 Solution View → 19

Let the solution curve of the differential equation x d y-y d x= x^ 2 +y^ 2 d x, x>0 , y(1)=0 , be y=y(x) . Then y(3) is equal to

JEE Main 2026 Solution View → 20

Let f:[1, ∞) arrow ℝ be a differentiable function. If 6 ∫_ 1 ^ x f(t) d t=3 x f(x)+x^ 3 -4 for all x ≥ 1 , then the value of f(2)-f(3) is

JEE Main 2026 Solution View → 21

Let y=y(x) be the solution of the differential equation x ~d y ~d x -2 y=2+3 x, x ∈(-(π)/(2), (π)/(2)) , y(0)=-(7)/(4) . Then y((π)/(6)) is equal to :

JEE Main 2026 Solution View → 22

Let y=y(x) be the solution curve of the differential equation (1+x^ 2 ) d y+(y- ^ -1 x) d x=0, y(0)=1 . Then the value of y(1) is :

JEE Main 2026 Solution View → 23

For all x>0 , let y_1(x), y_2(x) , and y_3(x) be the functions satisfying aligned & (d y_1)/(d x)-( x)^2 y_1=0, y_1(1)=5 & (d y_2)/(d x)-( x)^2 y_2=0, y_2(1)=(1)/(3) & (d y_3)/(d

JEE Advanced 2025 Solution View → 24

Let y(x) be the solution of the differential equation x^2 (d y)/(d x)+x y=x^2+y^2, x>(1)/(e) satisfying y(1)=0 . Then the value of 2 ((y(e))^2)/(y(e^2)) is _____ .

JEE Advanced 2025 Solution View → 25

Let f(x)=x-1 and g(x)=e^x for x ∈ ℝ . If (d y)/(d x)=(e^ -2 x g(f(f(x)))- y x ), y(0)=0 , then y(1) is :-

JEE Main 2025 Solution View → 26

Let y=y(x) be the solution of the differential equation (x^2+1) y^ -2 x y=(x^4+2 x^2+1) x , y(0)=1 . Then ∫_ -3 ^3 y(x) d x is :

JEE Main 2025 Solution View → 27

Let y=y(x) be the solution curve of the differential equation x(x^2+e^x) d y+(e^x(x-2) y-x^3) d x=0, x 0 passing through the point (1,0) . Then y(2) is equal to :

JEE Main 2025 Solution View → 28

If a curve y=y(x) passes through the point (1, (π)/(2)) and satisfies the differential equation (7 x^4 y-e^x cosec y) (d x)/(d y)=x^5, x ≥ 1 , then at x=2 , the value of cosy is:

JEE Main 2025 Solution View → 29

Let f:[0, ∞) arrow ℝ be differentiable function such that f(x)=1-2 x+∫_0^x e^ x-t f(t) dt for all x ∈[0, ∞) . Then the area of the region bounded by y=f(x) and the coordinate axes

JEE Main 2025 Solution View → 30

Let y=y(x) be the solution of the differential equation (d y)/(d x)+3( ^2 x) y+3 y= ^2 x y(0)=(1)/(3)+e^3 . Then y((π)/(4)) is equal to

JEE Main 2025 Solution View → 31

Let g be a differentiable function such that ∫_0^x g(t) d t=x-∫_0^x tg(t) d t, x ≥ 0 and let y=y(x) satisfy the differential equation (d y)/(d x)-y x= 2(x+1) x g(x), x ∈[0

JEE Main 2025 Solution View → 32

Let f:[1, ∞) arrow[2, ∞) be a differentiable function, If 10 ∫_1^ x f(t) dt=5 x f(x)-x^5-9 for all x ≥ 1 , then the value of f(3) is :

JEE Main 2025 Solution View → 33

Let y=y(x) be the solution of the differential equation (d y)/(d x)+2 y ^2 x=2 ^2 x+3 x · ^2 x such that y(0)=(5)/(4) . Then 12(y((π)/(4))-e^ -2 ) is equal to _______.

JEE Main 2025 Solution View → 34

Let f: R arrow R be a thrice differentiable odd function satisfying f^ (x) ≥ 0, f^ (x)=f(x), f(0)=0, f^ (0)=3 . Then 9 f( _ c 3) is equal to _______.

JEE Main 2025 Solution View → 35

If for the solution curve y=f(x) of the differential equation d y ~d x +( x) y=(2+ x)/((1+2 x)^2) , x ∈((-π)/(2), (π)/(2)), f((π)/(3))= 3 10 , then f((π)/(4)) is equal to :

JEE Main 2025 Solution View → 36

Let \(y=y(x)\) be the solution of the differential equation \( x( _ e ( x))^2 dy+( x-3 y x _ e ( x)) d x=0, x ∈(0, (π)/(2))\). If \(y((π)/(4))= -1 _ e 2 \), then \(y((π)/(6))\) is

JEE Main 2025 Solution View → 37

If y=y(x) is the solution of the differential equation, 4-x^2 ~d y ~d x =(( ^ -1 ((x)/(2)))^2-y) ^ -1 ((x)/(2)),-2 ≤ x ≤ 2, y(2)=(π^2-8)/(4) , then y^2(0) is equal to

JEE Main 2025 Solution View → 38

Let f:(0, ∞) arrow R be a function which is differentiable at all points of its domain and satisfies the condition x^2 f^ (x)=2 x f(x)+3 , with f(1)=4 . Then 2 f(2) is equal to :

JEE Main 2025 Solution View → 39

Let y=y(x) be the solution of the differential equation 2 x ~d y ~d x = 2 x-4 y x, x ∈(0, (π)/(2)) . If y((π)/(3))=0 , then y^ ((π)/(4))+y((π)/(4)) is equal to ________.

JEE Main 2025 Solution View → 40

Let y=y(x) be the solution of the differential equation (x y-5 x^2 1+x^2 ) d x+(1+x^2) d y=0, y(0)=0 . Then y( 3 ) is equal to

JEE Main 2025 Solution View → 41

Let f be a differentiable function such that 2(x+2)^2 f(x)-3(x+2)^2=10 ∫_0^x(t+2) f(t) d t, x ≥ 0 . Then f(2) is equal to ______.

JEE Main 2025 Solution View → 42

Let x=x(y) be the solution of the differential equation y=(x-y ~d x ~d y ) ((x)/(y)), y 0 and x(1)=(π)/(2) . Then (x(2)) is equal to :

JEE Main 2025 Solution View → 43

Let a curve y=f(x) pass through the points (0,5) and ( _e 2, k) . If the curve satisfies the differential equation 2(3+y) e^ 2 x d x-(7+e^ 2 x ) d y=0 , then k is equal to

JEE Main 2025 Solution View → 44

If x=f(y) is the solution of the differential equation (1+y^2)+(x-2 e^ ^ -1 y ) d y ~d x =0, y ∈(-(π)/(2), (π)/(2)) with f(0)=1 , then f( 1 3 ) is equal to :

JEE Main 2025 Solution View → 45

Let y=f(x) be the solution of the differential equation d y ~d x +(x y)/(x^2-1)= x^6+4 x 1-x^2 ,-1 x 1 such that f(0)=0 . If 6 ∫_ -1 / 2 ^ 1 / 2 f(x) d x=2 π-α then α^2 is equal

JEE Main 2025 Solution View → 46

Let x=x(y) be the solution of the differential equation y^2 ~d x+(x-(1)/(y)) d y=0 . If x(1)=1 , then x((1)/(2)) is :

JEE Main 2025 Solution View → 47

The solution curve, of the differential equation 2 y d y ~d x +3=5 d y ~d x , passing through the point (0,1) is a conic, whose vertex lies on the line:

JEE Main 2024 Solution View → 48

The solution of the differential equation (x^2+y^2) d x-5 x y ~d y=0, y(1)=0 , is :

JEE Main 2024 Solution View → 49

Let y=y(x) be the solution curve of the differential equation y d y ~d x +2 x y=x^3 y, y(1)=0 . Then y( 3 ) is equal to :

JEE Main 2024 Solution View → 50

Let α|x|=|y| e^ x y-β , α, β ∈ N be the solution of the differential equation x ~d y-y ~d x+x y(x ~d y+y ~d x)=0 , y(1)=2 . Then α+β is equal to ________

JEE Main 2024 Solution View → 51

Let y=y(x) be the solution of the differential equation (1+y^2) e^ x d x+ ^2 x(1+e^ 2 x ) d y=0, y(0)=1 . Then y((π)/(4)) is equal to

JEE Main 2024 Solution View → 52

Suppose the solution of the differential equation (d y)/(d x)=((2+α) x-β y+2)/(β x-2 α y-(β γ-4 α)) represents a circle passing through origin. Then the radius of this circle is :

JEE Main 2024 Solution View → 53

If the solution y(x) of the given differential equation (e^y+1) x ~d x+e^y x ~d y=0 passes through the point ((π)/(2), 0) , then the value of e^ y((π)/(6)) is equal to_________

JEE Main 2024 Solution View → 54

Let y=y(x) be the solution of the differential equation (1+x^2) (d y)/(d x)+y=e^ ^ -1 x , y(1)=0 . Then y(0) is

JEE Main 2024 Solution View → 55

Let y=y(x) be the solution of the differential equation (2 x _e x) (d y)/(d x)+2 y=(3)/(x) _e x, x>0 and y(e^ -1 )=0 . Then, y(e) is equal to

JEE Main 2024 Solution View → 56

The differential equation of the family of circles passing through the origin and having centre at the line y=x is :

JEE Main 2024 Solution View → 57

Let y=y(x) be the solution of the differential equation d y ~d x +(2 x)/((1+x^2)^2) y=x e^ (1)/((1+x^2)) ; y(0)=0 . Then the area enclosed by the curve f(x)=y(x) e^ -(1)/((1+x^2))

JEE Main 2024 Solution View → 58

If y=y(x) is the solution of the differential equation d y ~d x +2 y= (2 x), y(0)=(3)/(4) , then y((π)/(8)) is equal to:

JEE Main 2024 Solution View → 59

Let y=y(x) be the solution of the differential equation (x^2+4)^2 d y+(2 x^3 y+8 x y-2) d x=0 . If y(0)=0 , then y(2) is equal to

JEE Main 2024 Solution View → 60

Let y=y(x) be the solution of the differential equation (x+y+2)^2 d x=d y, y(0)=-2 . Let the maximum and minimum values of the function y=y(x) in [0, (π)/(3)] be α and β

JEE Main 2024 Solution View → 61

If the solution y=y(x) of the differential equation (x^4+2 x^3+3 x^2+2 x+2) d y-(2 x^2+2 x+3) d x=0 satisfies y(-1)=-(π)/(4) , then y(0) is equal to :

JEE Main 2024 Solution View → 62

Let the solution y=y(x) of the differential equation d y ~d x -y=1+4 x satisfy y(π)=1 . Then y((π)/(2))+10 is equal to ______

JEE Main 2024 Solution View → 63

Let α be a non-zero real number. Suppose f: R → R is a differentiable function such that f(0) = 1 and _ x → - ∞ f(x) = 1 . If f ^ ' (x) = (x) + 3 , for all x ∈ R, then f(- _ e 2)

JEE Main 2024 Solution View → 64

If (dx)/(dy) = 1 + x - y ^ 2 y , x(1) = 1, then 5x(2) is equal to:

JEE Main 2024 Solution View → 65

Let y = y(x) be the solution of the differential equation (dy)/(dx) = 2x (x + y) ^ 3 - x(x + y) - 1, y(0) = 1 . Then, ( 1 2 + y( 1 2 )) ^ 2 equals:

JEE Main 2024 Solution View → 66

If x = x (t) is the solution of the differential equation (t + 1)dx = (2x + (t + 1) ^ 4 )dt, x (0) = 2 , then x (1) equals ________

JEE Main 2024 Solution View → 67

Let y = y(x) be the solution of the differential equation sec ^ 2 xdx + ( e ^ 2y ^ 2 x + tanx)dy = 0, 0 < x < (π)/(2), y((π)/(4)) = 0 . If y((π)/(6)) = α , then e ^ 8α is equal to

JEE Main 2024 Solution View → 68

The temperature T(t) of a body at time t = 0 is 160 ^ ° F and it decreases continuously as per the differential equation (dT)/(dt) = - K(T - 80) , where K is positive constant. If

JEE Main 2024 Solution View → 69

The solution curve of the differential equation y(dx)/(dy) = x( _ e x - _ e y + 1), x > 0, y > 0 passing through the point ( e, 1 ) is

JEE Main 2024 Solution View → 70

Let y = y ( x ) be the solution of the differential equation (dy)/(dx) = ((tanx) + y)/(sinx(secx - sinxtanx)), x ∈ (0, (π)/(2)) satisfying the condition y((π)/(4)) = 2 . Then

JEE Main 2024 Solution View → 71

Let y = y ( x ) be the solution of the differential equation secxdy + \ 2(1 - x)tanx + x(2 - x)\ dx = 0 such that y(0) = 2 . Then y(2) is equal to :

JEE Main 2024 Solution View → 72

Let y = y ( x ) be the solution of the differential equation (1 - x ^ 2 )dy = [xy + ( x ^ 3 + 2) 3(1 - x ^ 2 ) ]dx , - 1 < x < 1, y ( 0 ) = 0 . If y((1)/(2)) = (m)/(n), m and n

JEE Main 2024 Solution View → 73

If sin((y)/(x)) = _ e | x | + (α)/(2) is the solution of the differential equation xcos((y)/(x))(dy)/(dx) = ycos((y)/(x)) + x and y ( 1 ) = (π)/(3) , then α ^ 2 is equal to

JEE Main 2024 Solution View → 74

If the solution curve y = y ( x ) of the differential equation (1 + y ^ 2 )(1 + _ e x)dx + xdy = 0, x > 0 passes through the point ( 1, 1 ) and y(e) = (α - tan((3)/(2)))/(β +

JEE Main 2024 Solution View → 75

A function y = f ( x ) satisfies f(x)sin2x + sinx - (1 + ^ 2 x) f ^ ' (x) = 0 with condition f ( 0 ) = 0 . Then f((π)/(2)) is equal to

JEE Main 2024 Solution View → 76

If y = y ( x ) is the solution curve of the differential equation ( x ^ 2 - 4)dy - ( y ^ 2 - 3y)dx = 0 , x > 2, y ( 4 ) = (3)/(2) and the slope of the curve is never zero, then

JEE Main 2024 Solution View → 77

If the solution curve, of the differential equation (dy)/(dx) = (x + y - 2)/(x - y) passing through the point ( 2, 1 ) is ^ - 1 ((y - 1)/(x - 1)) - (1)/(β) _ e (α + ((y - 1)/(x

JEE Main 2024 Solution View → 78

If the solution of the differential equation ( 2x + 3y - 2 ) dx + ( 4x + 6y - 7 ) dy = 0, y ( 0 ) = 3 , is + + 3 _ e | 2x + 3y - γ | = 6 , then α + 2β + 3γ is equal to ______.

JEE Main 2024 Solution View → 79

Let x = x ( t ) and y = y ( t ) be solutions of the differential equations (dx)/(dt) + ax = 0 and (dy)/(dt) + by = 0 respectively, a, b ∈ R . Given that x ( 0 ) = 2; y ( 0 ) = 1

JEE Main 2024 Solution View → 80

Let f: [ 1 . ∞ ) → ℝ be a differentiable function such that f(1) = (1)/(3) and 3 ∫ _ 1 ^ x f(t)dt = xf(x) - x ^ 3 3 , x ∈ [ 1, ∞ ) . Let e denote the base of the natural

JEE Advanced 2023 Solution View → 81

For x ∈ ℝ , let y(x) be a solution of the differential equation ( x ^ 2 - 5)(dy)/(dx) - 2xy = - 2x ( x ^ 2 - 5) ^ 2 such that y (2) = 7 . Then the maximum value of the function y

JEE Advanced 2023 Solution View → 82

Let x = x(y) be the solution of the differential equation 2(y + 2) _ e (y + 2)dx + (x + 4 - 2 _ e (y + 2))dy = 0 , y > - 1 with x( e ^ 4 - 2) = 1 . Then x( e ^ 9 - 2) is equal to

JEE Main 2023 Solution View → 83

If y = y ( x ) is the solution of the differential equation (dy)/(dx) + 4x ( x ^ 2 - 1) y = x + 2 ( x ^ 2 - 1)(5)/(2) , x > 1 such that y ( 2 ) = (2)/(9) _ e (2 + 3 ) and y( 2 ) =

JEE Main 2023 Solution View → 84

Let y = y _ 1 (x) and y = y _ 2 (x) be the solution curves the differential equation (dy)/(dx) = y + 7 with initial conditions y _ 1 (0) = 0 and y _ 2 (0) = 1 respectively. Then

JEE Main 2023 Solution View → 85

Let y = y(x), y > 0, be a solution curve of the differential equation (1 + x ^ 2 )dy = y(x - y)dx . If y(0) = 1 and y(2 2 ) = β, then

JEE Main 2023 Solution View → 86

Let y = y(x) be the solution of the differential equation (dy)/(dx) + 5 x( x ^ 5 + 1) y = ( x ^ 5 + 1) ^ 2 x ^ 7 , x > 0 . If y(1) = 2 , then y(2) is equal to

JEE Main 2023 Solution View → 87

Let y = y (x) be a solution curve of the differential equation, (1 - x ^ 2 y ^ 2 )dx = ydx + xdy , If the line x = 1 intersects the curve y = y (x) at y = 2 and the line x = 2

JEE Main 2023 Solution View → 88

Let the tangent at any point P on a curve passing through the points (1, 1) and ((1)/(10), 100) , intersect positive x -axis and y -axis at the points A and B respectively. If PA

JEE Main 2023 Solution View → 89

Let f be a differentiable function such that x ^ 2 f(x) - x = 4 ∫ _ 0 ^ x tf(t)dt, f(1) = (2)/(3) . Then 18f(3) is equal to

JEE Main 2023 Solution View → 90

The slope of tangent at any point (x, y) on a curve y = y(x) is x ^ 2 + y ^ 2 2xy , x > 0 . If y(2) = 0 , then a value of y(8) is

JEE Main 2023 Solution View → 91

Let the solution curve x = x ( y ) , 0 < y < (π)/(2) , of the differential equation ( _ e (cosy)) ^ 2 cosydx - (1 + 3x _ e (cosy))sinydy = 0 satisfy x((π)/(3)) = 1 2 _ e 2 . If

JEE Main 2023 Solution View → 92

If the solution curve of the differential equation ( y - 2 _ e x ) dx + ( x _ e x ^ 2 ) dy = 0, x > 1 passes through the points (e, (4)/(3)) and ( e ^ 4 , α ) , then α is equal to

JEE Main 2023 Solution View → 93

If the solution curve f ( x, y ) = 0 of the differential equation (1 + _ e x)(dx)/(dy) - x _ e x = e ^ y , x > 0, passes through the points ( 1, 0 ) and ( a, 2 ) , then a ^ a is

JEE Main 2023 Solution View → 94

Let y = y(x) be a solution of the differential equation ( xcosx ) dy + ( xysinx + ycosx - 1 ) dx = 0, 0 < x < (π)/(2) . If (π)/(3)y((π)/(3)) = 3 , then |(π)/(6) y ^ " ((π)/(6)) +

JEE Main 2023 Solution View → 95

Let = exp( x ^ β y ^ γ ) be the solution of the differential equation 2 x ^ 2 ydy - (1 - x y ^ 2 )dx = 0 , x > 0, y(2) = _ e 2 . Then α + β - γ equals :

JEE Main 2023 Solution View → 96

If y = y(x) is the solution curve of the differential equation (dy)/(dx) + ytanx = xsecx, 0 ≤ x ≤ (π)/(3), y(0) = 1 , then y((π)/(6)) is equal to

JEE Main 2023 Solution View → 97

Let f: ℝ → ℝ be a differentiable function such that f ^ ' (x) + f(x) = ∫ _ 0 ^ 2 f(t)dt . If f(0) = e ^ - 2 , then 2f(0) - f(2) is equal to _____ .

JEE Main 2023 Solution View → 98

Let y = y ( x ) be the solution of the differential equation (3 y ^ 2 - 5 x ^ 2 )ydx + 2x( x ^ 2 - y ^ 2 )dy = 0 such that y ( 1 ) = 1 . Then |( y ( 2 ) ) ^ 3 - 12y ( 2 )| is

JEE Main 2023 Solution View → 99

The solution of the differential equation (dy)/(dx) = - ( x ^ 2 + 3 y ^ 2 3 x ^ 2 + y ^ 2 ), y(1) = 0 is

JEE Main 2023 Solution View → 100

Let the solution curve y = y ( x ) of the differential equation (dy)/(dx) - 3 x ^ 5 ^ - 1 ( x ^ 3 ) (1 + x ^ 6 )(3)/(2) y = 2x exp x ^ 3 - ^ - 1 x ^ 3 ( 1 + x ) ^ 6 pass through

JEE Main 2023 Solution View → 101

Let y = y ( x ) be the solution of the differential equation x _ e x(dy)/(dx) + y = x ^ 2 _ e x, ( x > 1 ) . If y ( 2 ) = 2 , then y ( e ) is equal to

JEE Main 2023 Solution View → 102

Let y = f ( x ) be the solution of the differential equation y ( x + 1 ) dx - x ^ 2 dy = 0, y ( 1 ) = e . Then _ x → 0 ^ + f ( x ) is equal to

JEE Main 2023 Solution View → 103

Let y = y(t) be a solution of the differential equation (dy)/(dt) + = γ e ^ - Where, α > 0, β > 0 and γ > 0 . Then Lim _ t → ∞ y(t)

JEE Main 2023 Solution View → 104

Let y = y(x) be the solution curve of the differential equation (dy)/(dx) = (y)/(x)(1 + x ^ 2 (1 + _ e x)) , x > 0, y ( 1 ) = 3 . Then y ^ 2 ( x ) 9 is equal to :

JEE Main 2023 Solution View → 105

Let y = y ( x ) be the solution of the differential equation ( x ^ 2 – 3 y ^ 2 ) dx + 3xydy = 0, y ( 1 ) = 1 . Then 6 y ^ 2 (e) is equal to

JEE Main 2023 Solution View → 106

Let y = y ( x ) be the solution of the differential equation x ^ 3 dy + ( xy – 1 ) dx = 0, x > 0, y((1)/(2)) = 3 - e . Then y(1) is equal to

JEE Main 2023 Solution View → 107

If y(x) is the solution of the differential equation xdy - ( y ^ 2 - 4y)dx = 0 for x > 0, y(1) = 2 , and the slope of the curve y = y(x) is never zero, then the value of 10y( 2 )

JEE Advanced 2022 Solution View → 108

For x ∈ ℝ , let the function y(x) be the solution of the differential equation (dy)/(dx) + 12y = cos((π)/(12)x), y(0) = 0 . Then, which of the following statements is/are TRUE?

JEE Advanced 2022 Solution View → 109

If the solution curve of the differential equation (dy)/(dx) = (x + y - 2)/(x - y) passes through the point (2, 1) and (k + 1, 2), k > 0 , then

JEE Main 2022 Solution View → 110

Let y = y(x) be the solution curve of the differential equation (dy)/(dx) + ( 2 x ^ 2 + 11x + 13 x ^ 3 + 6 x ^ 2 + 11x + 6 )y = ((x + 3))/(x + 1), x > - 1 , which passes through

JEE Main 2022 Solution View → 111

Let the solution curve y = y(x) of the differential equation (1 + e ^ 2x )((dy)/(dx) +y) = 1 pass through the point (0, (π)/(2) ) . Then, _ x → ∞ e ^ x y (x) is equal to

JEE Main 2022 Solution View → 112

Let y = y(x) be the solution curve of the differential equation (dy)/(dx) + 1 x ^ 2 - 1 y = ((x - 1)/(x + 1))(1)/(2) , x > 1 passing through the point (2, (1)/(3) ) . Then 7 y(8)

JEE Main 2022 Solution View → 113

The differential equation of the family of circles passing through the points (0, 2) and (0, - 2) is

JEE Main 2022 Solution View → 114

Let the solution curve of the differential equation xdy = ( x ^ 2 + y ^ 2 + y)dx, x > 0 , intersect the line x = 1 at y = 0 and the line x = 2 at y = α . Then the value of α is

JEE Main 2022 Solution View → 115

If y = y(x) , x ∈ (0, (π)/(2)) be the solution curve of the differential equation ( ^ 2 2x)(dy)/(dx) + (8 ^ 2 2x + 2sin4x) y = 2 e ^ - 4x (2sin2x + cos2x) , with y ((π)/(4)) = e ^

JEE Main 2022 Solution View → 116

Let y = y _ 1 (x) and y = y _ 2 (x) be two distinct solutions of the differential equation (dy)/(dx) = x + y , with y _ 1 (0) = 0 and y _ 2 (0) = 1 respectively. Then, the number

JEE Main 2022 Solution View → 117

Let y = y(x) be the solution curve of the differential equation sin(2 x ^ 2 ) _ e (tan x ^ 2 )dy + (4xy - 4 2 xsin( x ^ 2 - (π)/(4)))dx = 0, 0 , which passes through the point (

JEE Main 2022 Solution View → 118

Let the solution curve y = f(x) of the differential equation (dy)/(dx) + xy x ^ 2 - 1 = x ^ 4 + 2x 1 - x ^ 2 , x ∈ (- 1, 1) pass through the origin. Then ∫ _ - 3 2 ^ 3 2 f(x)dx is

JEE Main 2022 Solution View → 119

Suppose y = y(x) be the solution curve to the differential equation (dy)/(dx) - y = 2 - e ^ - x such that _ x → ∞ y(x) is finite. If a and b are respectively the x - and y

JEE Main 2022 Solution View → 120

If (dy)/(dx) + 2ytanx = sinx, 0 < x < (π)/(2) and y((π)/(3)) = 0 , then the maximum value of y(x) is

JEE Main 2022 Solution View → 121

Let a smooth curve y = f(x) be such that the slope of the tangent at any point (x, y) on it is directly proportional to ((- y)/(x)) . If the curve passes through the points (1, 2)

JEE Main 2022 Solution View → 122

Let y = y(x) be the solution of the differential equation (dy)/(dx) = 4 y ^ 3 + 2y x ^ 2 3x y ^ 2 + x ^ 3 , y(1) = 1 . If for some n ∈ N, y(2) ∈ [ n - 1, n ) , then n is equal to

JEE Main 2022 Solution View → 123

The slope of the tangent to a curve C: y = y(x) at any point [ x, y ) on it is 2 e ^ 2x - 6 e ^ - x + 9 2 + 9 e ^ - 2x . If C passes through the points (0, (1)/(2) + π 2 2 ) and

JEE Main 2022 Solution View → 124

The general solution of the differential equation (x - y ^ 2 )dx + y(5x + y ^ 2 )dy = 0 is

JEE Main 2022 Solution View → 125

If y = y (x) is the solution of the differential equation (1 + e ^ 2x )(dy)/(dx) + 2(1 + y ^ 2 ) e ^ x = 0 and y(0) = 0 , then 6 (y ' (0) + (y( _ c 3 )) ^ 2 ) is equal to:

JEE Main 2022 Solution View → 126

Let y = y(x), x > 1 , be the solution of the differential equation (x - 1)(dy)/(dx) + 2xy = (1)/(x - 1) , with y(2) = 1 + e ^ 4 2 e ^ 4 . If y(3) = e ^ α + 1 β e ^ α . then the

JEE Main 2022 Solution View → 127

Let the solution curve of the differential equation x(dy)/(dx) - y = y ^ 2 + 16 x ^ 2 , y(1) = 3 be y = y(x) . Then y(2) is equal to

JEE Main 2022 Solution View → 128

Let y = y(x) be the solution of the differential equation (dy)/(dx) + 2 y 2 ^ 4 x - cos2x = x e ^ ^ - 1 ( 2 cot2x) , 0 < x < (π)/(2) with y((π)/(4)) = π ^ 2 32 . If y((π)/(3)) = π

JEE Main 2022 Solution View → 129

Let x = x(y) be the solution of the differential equation 2ye x y ^ 2 dx + ( y ^ 2 - 4xe x y ^ 2 )dy = 0 such that x(1) = 0 . Then, x(e) is equal to

JEE Main 2022 Solution View → 130

Let the slope of the tangent to a curve y = f(x) at (x, y) be given by 2tanx (cosx - y) . if the curve passes through the point ((π)/(4), 0) , then the value of ∫ _ 0 ^ (π)/(2)

JEE Main 2022 Solution View → 131

Let the solution curve y = y(x) of the differential equation, [ x x ^ 2 - y ^ 2 + e(y)/(x)]x(dy)/(dx) = x + [ x x ^ 2 - y ^ 2 + e(y)/(x)]y pass through the points (1, 0) and (2α

JEE Main 2022 Solution View → 132

Let y = y(x) be the solution of the differential equation x(1 - x ^ 2 )(dy)/(dx) + (3 x ^ 2 y - y - 4 x ^ 3 ) = 0, x > 1 with y(2) = - 2 . Then y(3) is equal to

JEE Main 2022 Solution View → 133

If the solution curve of the differential equation (( ^ - 1 y) - x)dy = (1 + y ^ 2 )dx passes through the point (1, 0) then the abscissa of the point on the curve whose ordinate

JEE Main 2022 Solution View → 134

Let y = y(x) be the solution of the differential equation (1 - x ^ 2 )dy = (xy + ( x ^ 3 + 2) 1 - x ^ 2 )dx, - 1 and y(0) = 0 . If ∫ _ - (1)/(2) ^ (1)/(2) 1 - x ^ 2 y(x)dx = k

JEE Main 2022 Solution View → 135

Let (dy)/(dx) = (ax - by + a)/(bx + cy + a) , where a, b, c are constants. represent a circle passing through the point (2, 5) . Then the shortest distance of the point (11, 6)

JEE Main 2022 Solution View → 136

If (dy)/(dx) + 2 ^ x - y ( 2 ^ y - 1) 2 ^ x - 1 = 0, x, y > 0, y(1) = 1 , then y(2) is equal to

JEE Main 2022 Solution View → 137

If y = y(x) is the solution of the differential equation x(dy)/(dx) + 2y = x e ^ x , y(1) = 0 then the local maximum value of the function z(x) = x ^ 2 y ( x ) - e ^ x , x ∈ R is

JEE Main 2022 Solution View → 138

If (dy)/(dx) + e ^ x ( x ^ 2 - 2)y = ( x ^ 2 - 2x)( x ^ 2 - 2) e ^ 2x and y(0) = 0 , then the value of y(2) is

JEE Main 2022 Solution View → 139

Let the solution curve y = y (x) of the differential equation (4 + x ^ 2 )dy - 2x( x ^ 2 + 3y + 4)dx = 0 pass through the origin. Then y(2) is equal to _____.

JEE Main 2022 Solution View → 140

Let S = (0, 2π) - \ (π)/(2), (3π)/(4), (3π)/(2), (7π)/(4)\ . Let y = y(x) , x ∈ S , be the solution curve of the differential equation (dy)/(dx) = (1)/(1 + sin2x), y((π)/(4)) =

JEE Main 2022 Solution View → 141

If y = y(x) is the solution of the differential equation 2 x ^ 2 (dy)/(dx) - 2xy + 3 y ^ 2 = 0 such that y(e) = (e)/(3) , then y(1) is equal to

JEE Main 2022 Solution View → 142

Let y = y (x) be the solution of the differential equation (x + 1) y ^ ' - y = e ^ 3x (x + 1) ^ 2 , with y (0) = (1)/(3) . Then, the point x = - (4)/(3) for the curvey = y(x) is

JEE Main 2022 Solution View → 143

If the solution curve y = y(x) of the differential equation y ^ 2 dx + ( x ^ 2 - xy + y ^ 2 ) dy = 0, which passes through the point (1, 1) and intersects the line y = 3 xat the

JEE Main 2022 Solution View → 144

The slope of normal at any point (x, y), x > 0, y > 0 on the curve y = y(x) is given by x ^ 2 xy - x ^ 2 y ^ 2 - 1 . If the curve passes through the point (1, 1) , then e · y(e)

JEE Main 2022 Solution View → 145

The surface area of a balloon of spherical shape being inflated, increases at a constant rate. If initially, the radius of balloon is 3 units and after 5 seconds, it becomes 7

JEE Main 2022 Solution View → 146

If x = x(y) is the solution of the differential equation y(dx)/(dy) = 2x + y ^ 3 (y + 1) e ^ y , x(1) = 0 ; then x(e) is equal to

JEE Main 2022 Solution View → 147

For any real numbers α and β , let y _ α, β (x), x ∈ R , be the solution of the differential equation (dy)/(dx) + = x e ^ , y(1) = 1 Let S = \ y _ α, β (x): α, β ∈ R\ . Then which

JEE Advanced 2021 Solution View → 148

If y = y ( x ) is the solution curve of the differential equation x ^ 2 dy + (y - (1)/(x))dx = 0; x > 0 and y ( 1 ) = 1, then y((1)/(2)) is equal to :

JEE Main 2021 Solution View → 149

If y(dy)/(dx) = x[ y ^ 2 x ^ 2 + ϕ( y ^ 2 x ^ 2 ) ϕ ^ ' ( y ^ 2 x ^ 2 ) ], x > 0, ϕ > 0, and y ( 1 ) = - 1, then ϕ( y ^ 2 4 ) is equal to:

JEE Main 2021 Solution View → 150

If (dy)/(dx) = 2 ^ x y + 2 ^ y · 2 ^ x 2 ^ x + 2 ^ x + y _ e 2 , y(0) = 0, then for y = 1, the value of x lies in the interval :

JEE Main 2021 Solution View → 151

If (dy)/(dx) = 2 ^ x + y - 2 ^ x 2 ^ y , y(0) = 1, then y ( 1 ) is equal to :

JEE Main 2021 Solution View → 152

If the solution curve of the differential equation (2x - 10 y ^ 3 )dy + ydx = 0 , passes through the points ( 0, 1 ) and ( 2, β ) , then β is a root of the equation?

JEE Main 2021 Solution View → 153

A differential equation representing the family of parabolas with axis parallel to y - axis and whose length of latus rectum is the distance of the point ( 2, - 3 ) from the line

JEE Main 2021 Solution View → 154

Let us consider a curve, y = f (x) passing through the point (- 2, 2) and the slope of the tangent to the curve at any point ( x, f ( x ) ) is given by f ( x ) + x f ^ ' ( x ) = x

JEE Main 2021 Solution View → 155

Let y = y ( x ) be the solution of the differential equation (dy)/(dx) = 2(y + 2sinx - 5)x - 2cosx such that y ( 0 ) = 7 . Then y ( π ) is equal to

JEE Main 2021 Solution View → 156

Let y ( x ) be the solution of the differential equation 2 x ^ 2 dy + ( e ^ y - 2x)dx = 0, x > 0 . If y ( e ) = 1, then y ( 1 ) is equal to:

JEE Main 2021 Solution View → 157

Let y = y ( x ) be a solution curve of the differential equation (y + 1) ^ 2 xdx + tanxdy + ydx = 0 , x ∈ (0, (π)/(2)) . If _ x → 0 ^ + xy(x) = 1 , then the value of y((π)/(4)) is:

JEE Main 2021 Solution View → 158

Let y = y (x) be the solution of the differential equation (x - x ^ 3 )dy = (y + y x ^ 2 - 3 x ^ 4 )dx, x > 2 If y(3) = 3, then y(4) is equal to:

JEE Main 2021 Solution View → 159

Let y = y(x) be the solution of the differential equation dy = e ^ + y dx; α ∈ N . If y( _ e 2) = _ e 2 and y(0) = _ e ((1)/(2)), then the value of α is equal to ___.

JEE Main 2021 Solution View → 160

Let y = y(x) be solution of the differential equation _ e ((dy)/(dx)) = 3x + 4y, with y(0) = 0 . If y(- (2)/(3) _ e 2) = α _ e 2 , then the value of α is equal to:

JEE Main 2021 Solution View → 161

If y = y(x), y ∈ [0, (π)/(2)) is the solution of the differential equation secy(dy)/(dx) - sin(x + y) - sin(x - y) = 0, with y(0) = 0 , then 5 y ^ ' ((π)/(2)) is equal to _____.

JEE Main 2021 Solution View → 162

Let y = y(x) be the solution of the differential equation xdy = (y + x ^ 3 cosx)dx with y(π) = 0, then y((π)/(2)) is equal to:

JEE Main 2021 Solution View → 163

Let y = y ( x ) be the solution of the differential equation (dy)/(dx) = 1 + x e ^ y - x , - 2 < x < 2 , y(0) = 0 , then the minimum value of y(x), x ∈ (- 2 , 2 ) is equal to :

JEE Main 2021 Solution View → 164

Let y = y ( x ) be solution of the following differential equation e ^ y (dy)/(dx) - 2 e ^ y sinx + sinx ^ 2 x = 0, y((π)/(2)) = 0 . If y(0) = _ e (α + β e ^ - 2 ) , then 4 ( α +

JEE Main 2021 Solution View → 165

Let y = y(x) be the solution of the differential equation cosec ^ 2 xdy + 2dx = (1 + ycos2x) cosec ^ 2 xdx, with y((π)/(4)) = 0 . Then, the value of (y(0) + 1) ^ 2 is equal to:

JEE Main 2021 Solution View → 166

Let y = y ( x ) be the solution of the differential equation ((x + 2) e ^ ((y + 1)/(x + 2)) + (y + 1))dx = (x + 2)dy, y(1) = 1 . If the domain of y = y(x) is an open interval ( α

JEE Main 2021 Solution View → 167

Let y = y ( x ) satisfies the equation (dy)/(dx) - |A| = 0, for all x > 0, where A = [ cases y & sinx & 1 0 & - 1 & 1 2 & 0 & (1)/(x) cases ] . If y ( π ) = π + 2, then the value

JEE Main 2021 Solution View → 168

Let a curve y = y (x) be given by the solution of the differential equationcos ((1)/(2) ^ - 1 ( e ^ - x ))dx = ( e ^ 2x - 1 )dy . If it intersects y -axis at y = - 1 , and the

JEE Main 2021 Solution View → 169

Let y = y(x) be the solution of the differential equation xtan((y)/(x))dy = (ytan((y)/(x)) - x)dx , - 1 ≤ x ≤ 1, y((1)/(2)) = (π)/(6) . Then the area of the region bounded by the

JEE Main 2021 Solution View → 170

Let y = y(x) be the solution of the differential equation e ^ x 1 - y ^ 2 dx + ((y)/(x))dy = 0, y(1) = - 1 Then the value of (y(3)) ^ 2 is equal to:

JEE Main 2021 Solution View → 171

Let y = y ( x ) be the solution of the differential equation (dy)/(dx) = (y + 1)((y + 1) e ^ x ^ 2 / 2 - x), 0 < x < 2 . 1 , with y ( 2 ) = 0 . Then the value of (dy)/(dx) at x =

JEE Main 2021 Solution View → 172

Let y = y ( x ) be the solution of the differential equation xdy - ydx = ( x ^ 2 - y ^ 2 ) dx, x ≥ 1 , with y ( 1 ) = 0 . If the area bounded by the line x = 1, x = e ^ π , y = 0

JEE Main 2021 Solution View → 173

The differential equation satisfied by the system of parabolas y ^ 2 = 4a ( x + a ) is

JEE Main 2021 Solution View → 174

Let y = y ( x ) be the solution of the differential equation cosx ( 3sinx + cosx + 3 ) dy = ( 1 + ysinx ( 3sinx + cosx + 3 ) ) dx, 0 ≤ x ≤ (π)/(2), y(0) = 0 . Then, y((π)/(3)) is

JEE Main 2021 Solution View → 175

If the curve y = y ( x ) is the solution of the differential equation 2( x ^ 2 + x ^ 5 / 4 )dy - y(x + x ^ 1 / 4 )dx = 2 x ^ 9 / 4 dx, x > 0 which passes through the point (1, 1

JEE Main 2021 Solution View → 176

Which of the following is true for y(x) that satisfies the differential equation (dy)/(dx) = xy - 1 + x - y; y(0) = 0

JEE Main 2021 Solution View → 177

If y = y(x) is the solution of the differential equation (dy)/(dx) + (tanx)y = sinx, 0 ≤ x ≤ (π)/(3), with y(0) = 0, then y((π)/(4)) is equal to

JEE Main 2021 Solution View → 178

Let C _ 1 be the curve obtained by the solution of differential equation 2xy(dy)/(dx) = y ^ 2 - x ^ 2 , x > 0 . Let the curve C _ 2 be the solution of 2xy x ^ 2 - y ^ 2 =

JEE Main 2021 Solution View → 179

If y = y(x) is the solution of the differential equation, (dy)/(dx) + 2ytanx = sinx, y((π)/(3)) = 0 , then the maximum value of the function y(x) over R is equal to :

JEE Main 2021 Solution View → 180

Let slope of the tangent line to a curve at any point P(x, y) be given by x y ^ 2 + y x . If the curve intersects the line x + 2y = 4 at x = - 2 , then the value of y , for which

JEE Main 2021 Solution View → 181

The rate of growth of bacteria in a culture is proportional to the number of bacteria present and the bacteria count is 1000 at initial time t = 0 . The number of bacteria is

JEE Main 2021 Solution View → 182

The difference between degree and order of a differential equation that represents the family of curves given by y ^ 2 = a(x + a 2 ), a > 0 is _______.

JEE Main 2021 Solution View → 183

If y = y(x) is the solution of the equation e ^ siny cosy(dy)/(dx) + e ^ siny cosx = cosx, y(0) = 0 ; then 1 + y((π)/(6)) + 3 2 y((π)/(3)) + 1 2 y((π)/(4)) is equal to _______.

JEE Main 2021 Solution View → 184

If the curve, y = y (x) represented by the solution of the differential equation (2x y ^ 2 - y)dx + xdy = 0 , passes through the intersection of the lines, 2x - 3y = 1 and 3x + 2y

JEE Main 2021 Solution View → 185

If a curve passes through the origin and the slope of the tangent to it at any point (x, y) is x ^ 2 - 4x + y + 8 x - 2 , then this curve also passes through the point:

JEE Main 2021 Solution View → 186

Let f be a twice differentiable function defined on R such that f(0) = 1, f ^ ' (0) = 2 and f ^ ' (x) ≠ 0 for all x ∈ R . If | cases f(x) & f ^ ' (x) f ^ ' (x) & f ^ '' (x) cases

JEE Main 2021 Solution View → 187

If a curve y = f(x) passes through the point (1, 2) and satisfies x (dy)/(dx) + y = b x ^ 4 , then for what value of b, ∫ _ 1 ^ 2 f (x) dx = (62)/(5) ?

JEE Main 2021 Solution View → 188

Let f(x) be a differentiable function defined on [0, 2] such that f ^ ' (x) = f ^ ' (2 - x) for allx ∈ (0, 2) , f (0) = 1 and f (2) = e ^ 2 . Then the value of ∫ _ 0 ^ 2 f (x) dx

JEE Main 2021 Solution View → 189

The population P = P(t) at time t of a certain species follows the differential equation (dP)/(dt) = 0 . 5P - 450 . If P(0) = 850 , then the time at which population becomes zero

JEE Main 2021 Solution View → 190

Let b be a nonzero real number. Suppose f: ℝ → ℝ is a differentiable function such that f(0) = 1 . If the derivative f ^ ' of f satisfies the equation f ^ ' (x) = f(x) b ^ 2 + x ^

JEE Advanced 2020 Solution View → 191

If y = ((2)/(π)x - 1)cosecx is the solution of the differential equation, (dy)/(dx) + p(x)y = - (2)/(π)cosecx, 0 < x < (π)/(2) , then the function p(x) is equal to :

JEE Main 2020 Solution View → 192

The general solution of the differential equation 1 + x ^ 2 + y ^ 2 + x ^ 2 y ^ 2 + xy(dy)/(dx) = 0 (where C is a constant of integration)

JEE Main 2020 Solution View → 193

Let y = y ( x ) be the solution of the differential equation cosx(dy)/(dx) + 2ysinx = sin2x, x ∈ (0, (π)/(2)) If y ( π / 3 ) = 0, then y ( π / 4 ) is equal to :

JEE Main 2020 Solution View → 194

If y = y(x) is the solution of the differential equation 5 + e ^ x 2 + y ⋅ (dy)/(dx) + e ^ x = 0 satisfying y(0) = 1 then value of y ( _ e 13 ) is

JEE Main 2020 Solution View → 195

The solution of the differential equation (dy)/(dx) - y + 3x _ e ( y + 3x ) + 3 = 0 is (where C is a constant of integration)

JEE Main 2020 Solution View → 196

Let y = y ( x ) be the solution of the differential equation, x y ^ ' - y = x ^ 2 ( xcosx + sinx ) , x > 0 . If y ( π ) = π, then y ' ' ((π)/(2)) + y((π)/(2)) is equal to :

JEE Main 2020 Solution View → 197

If x ^ 3 dy + xy · dx = x ^ 2 dy + 2ydx; y(2) = e and x > 1 , then y(4) is equal to :

JEE Main 2020 Solution View → 198

The solution curve of the differential equation, (1 + e ^ - x )(1 + y ^ 2 )(dy)/(dx) = y ^ 2 which passes through the point (0, 1) , is

JEE Main 2020 Solution View → 199

If a curve y = f (x), passing through the point (1, 2), is the solution of the differential equation 2 x ^ 2 dy = (2xy + y ^ 2 ) dx , then f ((1)/(2) ) is equal to

JEE Main 2020 Solution View → 200

Let y = y (x) be the solution of the differential equation, (2 + sinx)/(y + 1) . (dy)/(dx) =- cosx , y > 0, y(0) = 1 . If y(π) = a and (dy)/(dx) at x = π is b, then the ordered

JEE Main 2020 Solution View →
Practice all Differential Equations questions in the app →

Related JEE Mathematics chapters

Application of Derivatives (795)Three Dimensional Geometry (756)Sequences and Series (748)Functions (700)Definite Integration (692)Vector Algebra (616)Continuity and Differentiability (576)Probability (561)Complex Number (551)Binomial Theorem (550)Quadratic Equation (517)Determinants (508)

Differential Equations in other exams

NDA Differential Equations (127)BITSAT Differential Equations (27)