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Differential Equations — JEE Main & Advanced Mathematics PYQs

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

586 questionsMathematicsSolutions on every page
1

Let y : (- , ) (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 statement

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 ⁻¹x )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 < 2 , y ( 4 ) = 6 2 5 . If y ( 3 ) = 4 5 , then ^4 equals _______.

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) = 2 and let = ( y(e¹²) e¹² ) . Then the number of integral values of p , for which

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 y(1)= (2+e⁻²) , th

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 ( , -1 2 ) , then a value of

JEE Main 2026 Solution View → 12

Let y=y(x) be the solution of the differential equation x ~d y ~d x -y=x² x, x (0, ) . If y ( 2 )= 2 , then 6 y ( 6 )-8 y ( 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=x³ (2-x³ ) 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 x ( t² y(x)-x² 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 (x²-4 ) y^ -2 x y+2 x (4-x² )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 x⁴ ~d y+ (4 x³ y+2 x ) d x=0, x>0, y ( 2 )=0 . Then ⁴ y ( 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)= 2 , y(49)= , then 2 is equal to :

JEE Main 2026 Solution View → 19

Let the solution curve of the differential equation x d y-y d x= x²+y² 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, ) R be a differentiable function. If 6 ₁^ x f(t) d t=3 x f(x)+x³-4 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 (- 2 , 2 ) , y(0)=- 7 4 . Then y ( 6 ) is equal to :

JEE Main 2026 Solution View → 22

Let y=y(x) be the solution curve of the differential equation (1+x² ) 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 y₁(x), y₂(x) , and y₃(x) be the functions satisfying aligned & d y₁ d x -( x)^2 y₁=0, y₁(1)=5 & d y₂ d x -( x)^2 y₂=0, y₂(1)= 1 3 & d y₃ d x - ( 2-x^3 x^3 ) y₃=0,

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, 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, ) 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 is

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 ( 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, 2 ) . If y(0)=0

JEE Main 2025 Solution View → 32

Let f:[1, ) [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 ( 4 )- e ⁻² ) is equal to _______.

JEE Main 2025 Solution View → 34

Let f: R 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 ( - 2 , 2 ), f ( 3 )= 3 10 , then f ( 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, 2 ) ). If (y ( 4 )= -1 _ e 2 ), then (y ( 6 ) ) is equal to :

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)= ^2-8 4 , then y^2(0) is equal to

JEE Main 2025 Solution View → 38

Let f:(0, ) 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, 2 ) . If y ( 3 )=0 , then y^ ( 4 )+y ( 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)= 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 (- 2 , 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 - then ^2 is equal to _____

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 |x|=|y| e ^ x y- , , 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 + 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 ( 4 ) is equal to

JEE Main 2024 Solution View → 52

Suppose the solution of the differential equation d y d x = (2+ ) x- y+2 x-2 y-( -4 ) 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 ( 2 , 0 ) , then the value of e ^ y ( 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 ) and t

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 ( 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, 3 ] be and , respectively. If

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)=- 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( )=1 . Then y ( 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 lim x → − ∞ f x = 1 . If f ' x = α f x + 3 , for all x ∈ R , then f − log e 2

JEE Main 2024 Solution View → 64

If d x d y = 1 + x − y 2 y , x 1 = 1 , then 5 x 2 is equal to:

JEE Main 2024 Solution View → 65

Let y = y x be the solution of the differential equation d y d x = 2 x 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 d x = 2 x + t + 1 4 d t , 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 x d x + e 2 y tan 2 x + tan x d y = 0 , 0 < x < π 2 , y π 4 = 0 . If y π 6 = α , then e 8 α 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 d T d t = − K T − 80 , where K is positive constant. If T 15 =

JEE Main 2024 Solution View → 69

The solution curve of the differential equation y d x d y = x log e x - log 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 d y d x = tan x + y sin x sec x - sin x tan x , x ∈ 0 , π 2 satisfying the condition y π 4 = 2 . Then, y π 3 is

JEE Main 2024 Solution View → 71

Let y = y ( x ) be the solution of the differential equation sec x d y + 2 1 - x tan x + x 2 - x d x = 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 d y = x y + x 3 + 2 3 1 - x 2 d x , - 1 < x < 1 , y ( 0 ) = 0 . If y 1 2 = m n , m and n are coprime numbers, t

JEE Main 2024 Solution View → 73

If sin y x = log e | x | + α 2 is the solution of the differential equation x cos y x d y d x = y cos 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 + log e x d x + x d y = 0 , x > 0 passes through the point ( 1 , 1 ) and y e = α - tan 3 2 β + tan 3 2 , th

JEE Main 2024 Solution View → 75

A function y = f ( x ) satisfies f x sin 2 x + sin x - 1 + cos 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 - 3 y dx = 0 , x > 2 , y ( 4 ) = 3 2 and the slope of the curve is never zero, then the value of

JEE Main 2024 Solution View → 77

If the solution curve, of the differential equation d y d x = x + y - 2 x - y passing through the point ( 2 , 1 ) is tan - 1 y - 1 x - 1 - 1 β log e α + y - 1 x - 1 2 = log e x - 1

JEE Main 2024 Solution View → 78

If the solution of the differential equation ( 2 x + 3 y - 2 ) d x + ( 4 x + 6 y - 7 ) d y = 0 , y ( 0 ) = 3 , is α x + β y + 3 log e | 2 x + 3 y - γ | = 6 , then α + 2 β + 3 γ is

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 and 3 y

JEE Main 2024 Solution View → 80

Let f : [ 1 . &#8734; ) &#8594; &#8477; be a differentiable function such that f 1 = 1 3 and 3 &#8747; 1 x f t d t = x f x - x 3 3 , x &#8712; [ 1 , &#8734; ) . Let e denote the ba

JEE Advanced 2023 Solution View → 81

For x &#8712; &#8477; , let y x be a solution of the differential equation x 2 - 5 d y d x - 2 x y = - 2 x x 2 - 5 2 such that y 2 = 7 . Then the maximum value of the function y x

JEE Advanced 2023 Solution View → 82

Let x = x y be the solution of the differential equation 2 y + 2 log e y + 2 d x + x + 4 - 2 log e y + 2 d y = 0 , y &#62; - 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 d y d x + 4 x x 2 - 1 y = x + 2 x 2 - 1 5 2 , x &#62; 1 such that y ( 2 ) = 2 9 log e 2 + 3 and y 2 = &#945; log e &#945

JEE Main 2023 Solution View → 84

Let y = y 1 x and y = y 2 x be the solution curves the differential equation d y d x = y + 7 with initial conditions y 1 0 = 0 and y 2 0 = 1 respectively. Then the curves y = y 1 x

JEE Main 2023 Solution View → 85

Let y = y x , y &#62; 0 , be a solution curve of the differential equation 1 + x 2 d y = y x - y d x . If y 0 = 1 and y 2 2 = &#946; , then

JEE Main 2023 Solution View → 86

Let y = y x be the solution of the differential equation d y d x + 5 x x 5 + 1 y = x 5 + 1 2 x 7 , x &#62; 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 d x = y d x + x d y , If the line x = 1 intersects the curve y = y x at y = 2 and the line x = 2 intersect

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 P A : P B

JEE Main 2023 Solution View → 89

Let f be a differentiable function such that x 2 f x - x = 4 &#8747; 0 x t f t d t , f 1 = 2 3 . Then 18 f 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 2 x y , x &#62; 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 &#60; y &#60; &#960; 2 , of the differential equation log e cos y 2 cos y d x - 1 + 3 x log e cos y sin y d y = 0 satisfy x &#960; 3 = 1 2 lo

JEE Main 2023 Solution View → 92

If the solution curve of the differential equation ( y - 2 log e x ) d x + ( x log e x 2 ) d y = 0 , x &#62; 1 passes through the points e , 4 3 and ( e 4 , &#945; ) , then &#945;

JEE Main 2023 Solution View → 93

If the solution curve f ( x , y ) = 0 of the differential equation 1 + log e x d x d y - x log e x = e y , x &#62; 0 , passes through the points ( 1 , 0 ) and ( a , 2 ) , then a a

JEE Main 2023 Solution View → 94

Let y = y x be a solution of the differential equation ( x cos x ) d y + ( x y sin x + y cos x - 1 ) d x = 0 , 0 &#60; x &#60; &#960; 2 . If &#960; 3 y &#960; 3 = 3 , then &#960; 6

JEE Main 2023 Solution View → 95

Let &#945; x = exp x &#946; y &#947; be the solution of the differential equation 2 x 2 y d y - 1 - x y 2 d x = 0 , x &#62; 0 , y 2 = log e 2 . Then &#945; + &#946; - &#947; equals

JEE Main 2023 Solution View → 96

If y = y x is the solution curve of the differential equation d y d x + y tan x = x sec x , 0 &#8804; x &#8804; &#960; 3 , y 0 = 1 , then y &#960; 6 is equal to

JEE Main 2023 Solution View → 97

Let f : &#8477; &#8594; &#8477; be a differentiable function such that f ' x + f x = &#8747; 0 2 f t d t . If f 0 = e - 2 , then 2 f 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 y d x + 2 x x 2 - y 2 d y = 0 such that y ( 1 ) = 1 . Then ( y ( 2 ) ) 3 - 12 y ( 2 ) is equal to :

JEE Main 2023 Solution View → 99

The solution of the differential equation d y d x = - 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 d y d x - 3 x 5 tan - 1 x 3 1 + x 6 3 2 y = 2 x exp x 3 - tan - 1 x 3 ( 1 + x ) 6 pass through the origin. Then y (

JEE Main 2023 Solution View → 101

Let y = y ( x ) be the solution of the differential equation x log e x d y d x + y = x 2 log e x , ( x &#62; 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 ) d x - x 2 d y = 0 , y ( 1 ) = e . Then lim x &#8594; 0 + f ( x ) is equal to

JEE Main 2023 Solution View → 103

Let y = y t be a solution of the differential equation d y d t + &#945; y = &#947; e - &#946; t Where, &#945; &#62; 0 , &#946; &#62; 0 and &#947; &#62; 0 . Then Lim t &#8594; &#873

JEE Main 2023 Solution View → 104

Let y = y x be the solution curve of the differential equation d y d x = y x 1 + x 2 1 + log e x , x &#62; 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 &#8211; 3 y 2 ) dx + 3 xy dy = 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 d y + ( x y &#8211; 1 ) d x = 0 , x &#62; 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 x d y - y 2 - 4 y d x = 0 for x &#62; 0 , y 1 = 2 , and the slope of the curve y = y x is never zero, then the value of 10 y 2 i

JEE Advanced 2022 Solution View → 108

For x &#8712; &#8477; , let the function y x be the solution of the differential equation d y d x + 12 y = cos &#960; 12 x , y 0 = 0 . Then, which of the following statements is/ar

JEE Advanced 2022 Solution View → 109

If the solution curve of the differential equation d y d x = x + y - 2 x - y passes through the point 2 , 1 and k + 1 , 2 , k &#62; 0 , then

JEE Main 2022 Solution View → 110

Let y = y x be the solution curve of the differential equation d y d x + 2 x 2 + 11 x + 13 x 3 + 6 x 2 + 11 x + 6 y = x + 3 x + 1 , x &#62; - 1 , which passes through the point 0 ,

JEE Main 2022 Solution View → 111

Let the solution curve y = y x of the differential equation 1 + e 2 x d y d x + y = 1 pass through the point 0 , &#960; 2 . Then, lim x &#8594; &#8734; 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 d y d x + 1 x 2 - 1 y = x - 1 x + 1 1 2 , x &#62; 1 passing through the point 2 , 1 3 . Then 7 y 8 is equal to

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 x d y = x 2 + y 2 + y d x , x &#62; 0 , intersect the line x = 1 at y = 0 and the line x = 2 at y = &#945; . Then the value of &

JEE Main 2022 Solution View → 115

If y = y x , x &#8712; 0 , &#960; 2 be the solution curve of the differential equation sin 2 2 x d y d x + 8 sin 2 2 x + 2 sin 4 x y = 2 e - 4 x 2 sin 2 x + cos 2 x , with y &#960;

JEE Main 2022 Solution View → 116

Let y = y 1 x and y = y 2 x be two distinct solutions of the differential equation d y d x = x + y , with y 1 0 = 0 and y 2 0 = 1 respectively. Then, the number of points of inters

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Let y = y x be the solution curve of the differential equation sin 2 x 2 log e tan x 2 d y + 4 x y - 4 2 x sin x 2 - &#960; 4 d x = 0 , 0 &#60; x &#60; &#960; 2 , which passes thro

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Let the solution curve y = f x of the differential equation d y d x + x y x 2 - 1 = x 4 + 2 x 1 - x 2 , x &#8712; - 1 , 1 pass through the origin. Then &#8747; - 3 2 3 2 f x d x is

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Suppose y = y x be the solution curve to the differential equation d y d x - y = 2 - e - x such that lim x &#8594; &#8734; y x is finite. If a and b are respectively the x - and y

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If d y d x + 2 y tan x = sin x , 0 &#60; x &#60; &#960; 2 and y &#960; 3 = 0 , then the maximum value of y x is

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