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Differential Equations — NDA Mathematics PYQs

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

127 questionsMathematicsSolutions on every page
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Passage: Consider the differential equation e^ x+y dy dx =e^ x-y . Question: What is d^2y dx^2 ( dx dy )^2 equal to ?

NDA 2026 Solution View → 2

What is the solution of the differential equation ( dy dx )=p when y(0)=q ?

NDA 2026 Solution View → 3

Passage: Consider the differential equation e^ x+y dy dx =e^ x-y . Question: What is the solution of the differential equation with y(0)=0 ?

NDA 2026 Solution View → 4

What is the degree of the differential equation ( d^2y dx^2 )^ 3 2 = ( dy dx )^ 5 2 ?

NDA 2025 Solution View → 5

If k is an arbitrary constant, then what is the general solution of the equation (x + y)^2 dy dx = k^2 ?

NDA 2025 Solution View → 6

Consider the following statements: I. y = xe^ 2x is the solution of dy dx = y (2 + 1 x ) . II. y = x |x| + cx is the solution of dy dx = x + y x . Which of the statements given abo

NDA 2025 Solution View → 7

What are the order and degree respectively of the differential equation 2- ( d y d x )^2 ^ 0.6 = d^2 y d x^2 ?

NDA 2024 Solution View → 8

Paragraph: Let y d x+ (x-y^3 ) d y=0 be a differential equation. Question: What is the solution of the differential equation?

NDA 2024 Solution View → 9

The differential equation, representing the curve y=e^x(a x+b x) where a and b are arbitrary constants, is:

NDA 2024 Solution View → 10

Paragraph: Let y d x+ (x-y^3 ) d y=0 be a differential equation. Question: What are the order and degree respectively of the differential equation?

NDA 2024 Solution View → 11

If d y d x =2 e^x y^3, y(0)= 1 2 then what is 4 y^2 (2-e^x ) equal to?

NDA 2024 Solution View → 12

Let y₁(x) and y₂(x) be two solutions of the differential equation d y d x =x . If y₁(0)=0 and y₂(0)=4 , then what is the number of points of intersection of curves y₁(x) and y₂(x)

NDA 2024 Solution View → 13

A parabola pases through (1,2) and satisfies the differential equation d y d x = 2 y x , x 0, y 0 . What is the directrix of the parabola?

NDA 2023 Solution View → 14

A parabola pases through (1,2) and satisfies the differential equation d y d x = 2 y x , x 0, y 0 . What is the length of latus rectum of the parabola?

NDA 2023 Solution View → 15

What are the order and the degree respectively of the differential equation x^2 ( d^3 y d x^3 )^2+ ( d y d x )^4+ x=0 ?

NDA 2023 Solution View → 16

What is the differential equation of all parabolas of the type y^2=4 a(x-b) ?

NDA 2023 Solution View → 17

Paragraph: Suppose E is the differential equation representing family of curves y^2=2 c x+2 c c where c is a positive parameter. Question: What is the order of the differential equ

NDA 2023 Solution View → 18

A solution of the differential equation ( d y d x )^2-x d y d x =0 is

NDA 2023 Solution View → 19

Paragraph: Let f(x)=P e^x+Q e^ 2 x +R e^ 3 x , where P, Q, R are real numbers. Further f(0)=6, f^ ( 3)=282 and ₀^ 2 f(x) d x=11 Question: What is f^ (0) equal to?

NDA 2023 Solution View → 20

Paragraph: Suppose E is the differential equation representing family of curves y^2=2 c x+2 c c where c is a positive parameter. Question: What is the degree of the differential eq

NDA 2023 Solution View → 21

Consider the following statements : 1. The degree of the differential d y d x + ( d y d x )=0 is 1 . 2. The order of the differential equation ( d^2 y d x^2 )^3+ ( d y d x )=0 is 2

NDA 2022 Solution View → 22

What is the degree of the differential equation 1+ ( d y d x )^2= ( d^2 y d x^2 )^ 4 3 ?

NDA 2022 Solution View → 23

A radioactive substance decays at a rate proportional to the amount of substance present. If half of the substance decays in 100 years, then what is the decay constant (proportiona

NDA 2022 Solution View → 24

If d y d x =( n 5) y with y(0)= 5 , then what is y(1) equal to?

NDA 2022 Solution View → 25

What does the equation x d y d x -2 y=0 represent?

NDA 2022 Solution View → 26

What is the differential equation of the family of parabolas having vertex at origin and axis along positive y -axis ?

NDA 2022 Solution View → 27

What is the solution of the differential equation (d y-d x)+ x(d y+d x)=0 ?

NDA 2022 Solution View → 28

What is the order of the differential equation of all ellipses whose axes are along the coordinate axes?

NDA 2021 Solution View → 29

What is the degree of the differential equation of all circles touching both the coordinate axes in the first quadrant?

NDA 2021 Solution View → 30

A particle starts from origin with a velocity (in m / s ) given by the equation d x d t =x+1 . The time (in second) taken by the particle to traverse a distance of 24 m is

NDA 2021 Solution View → 31

If the general solution of a differential equation is y^2+2 c y-c x+c^2=0 , where c is an arbitrary constant, then what is the order of the differential equation?

NDA 2021 Solution View → 32

What is the degree of the following differential equation? x= 1+ d^2 y d x^2

NDA 2021 Solution View → 33

What is the solution of the following differential equation? ( d y d x )+y=x

NDA 2021 Solution View → 34

What is the differential equation of y=A- B x ?

NDA 2021 Solution View → 35

Which one of the following differential equations has the general solution y=a e^x+b e^ -x ?

NDA 2021 Solution View → 36

The function u(x, y)=c which satisfies the differential equation x(d x-d y)+y(d y-d x)=0 , is

NDA 2020 Solution View → 37

What is the solution of the differential equation ( d y d x )=x ?

NDA 2020 Solution View → 38

The solution of the differential equation d y= (1+y^2 ) d x is

NDA 2020 Solution View → 39

The order and degree of the differential equation k d y d x = [1+ ( d y d x )^2 ]^ 2 3 d x are respectively

NDA 2020 Solution View → 40

Which one of the following is the differential equation that represents the family of curves y= 1 2 x^2-c where c is an arbitrary constant?

NDA 2019 Solution View → 41

What is the degree of the differential equation d^3 y d x^3 + ( d y d x )^2-x^2 ( d^4 y d x^4 )=0 ?

NDA 2019 Solution View → 42

The differential equation which represents the family of curves given by y=c (1-e^x ) is

NDA 2019 Solution View → 43

The solution of the differential equation d y d x = ( y - x )+1 is

NDA 2019 Solution View → 44

The differential equation of the system of circles touching the y -axis at the origin is

NDA 2019 Solution View → 45

Consider the following in respect of the differential equation : d^2 y d x^2 +2 ( d y d x )^2+9 y=x 1. The degree of the differential equation is 1 . 2. The order of the differenti

NDA 2019 Solution View → 46

What is the general solution of the differential equation d y d x + x y =0 ?

NDA 2019 Solution View → 47

What is the solution of the differential equation ( d y d x )=a x+b y ?

NDA 2018 Solution View → 48

What is the order of the differential equation whose solution is y = a x + b x + ce ^ - x + d , where a , b , c and d are arbitrary constants?

NDA 2018 Solution View → 49

The differential equation of the family of curves y=p (a x)+ q ( ax ) , where p , q are arbitrary constants, is

NDA 2018 Solution View → 50

Which one of the following differential equations has a periodic solution?

NDA 2018 Solution View → 51

What is the solution of the differential equation d x d y = x+y+1 x+y-1 ?

NDA 2018 Solution View → 52

The order and degree of the differential equation y^2=4 a(x-a) , where ' a ' is an arbitrary constant, are respectively

NDA 2018 Solution View → 53

What is the solution of (1+2 x) d y-(1-2 y) d x=0 ?

NDA 2018 Solution View → 54

The equation of the curve passing through the point (-1,-2) which satisfies d y d x =-x^2- 1 x^3 is

NDA 2018 Solution View → 55

What is the solution of the differential equation x d y-y d x=0 ?

NDA 2018 Solution View → 56

What are the order and degree, respectively, of the differential equation ( d^3 y d x^3 )^2=y^4+ ( d y d x )^5 ?

NDA 2018 Solution View → 57

The order and degree of the differential equation [1+ ( d y d x )^2 ]^3= ^2 [ d^2 y d x^2 ]^2 are respectively

NDA 2017 Solution View → 58

The general solution of d y d x = a x+h b y+k represents a circle only when

NDA 2017 Solution View → 59

The differential equation of minimum order by eliminating the arbitrat constants A and C in the equatic y = A [ ( x + C )+ ( x + C )] is

NDA 2017 Solution View → 60

What is the general solution of the differential equation y d x- (x+2 y^2 ) d y=0 ?

NDA 2017 Solution View → 61

The solution of the differential equation d y d x = y ^ (x)-y^2 (x) is

NDA 2017 Solution View → 62

If x d y=y(d x+y d y) ; y(1)=1 and y(x) 0 , then what is y(-3) equal to?

NDA 2017 Solution View → 63

What is the solution of the differential equation ( dy dx )- a =0 ?

NDA 2017 Solution View → 64

What are the degree and order respectively of the differential equation y=x ( d y d x )^2+ ( d x d y )^2 ?

NDA 2017 Solution View → 65

What is the differential equation corresponding to y^2-2 a y+x^2=a^2 by eliminating a ?

NDA 2017 Solution View → 66

What are the degree and order respectively of the differential equation satisfying e ^ y 1- x ^2 + x 1- y ^2 =c e ^ x , (where c 0,| x | 1,| y | 1) ?

NDA 2016 Solution View → 67

What is the curve which passes through the point (1,1) and whose slope is 2 y x ?

NDA 2016 Solution View → 68

If x d y=y d x+y^2 d y, y 0 and y(1)=1 , then what is y(-3) equal to?

NDA 2016 Solution View → 69

What is the order of the differential equation dx dy + ydx = x ^3 ?

NDA 2016 Solution View → 70

What are the order and degree respectively of the differential equation whose solution is y = cx + c ^2-3 c ^ 3 / 2 +2 , where c is a parameter?

NDA 2016 Solution View → 71

Which one of the following differential equations represents the family of straight lines which are at unit distance from the origin?

NDA 2016 Solution View → 72

The degree of the differential equation d y d x -x= (y-x d y d x )⁻⁴ is

NDA 2015 Solution View → 73

The solution of d y d x = 1-x^2-y^2+x^2 y^2 is where c is an arbitrary constant.

NDA 2015 Solution View → 74

The differential equation of the family of circles passing through the origin and having centres on the x -axis is

NDA 2015 Solution View → 75

The order and degree of the differential equation of parabolas having vertex at the origin and focus at (a, 0) where a 0 , are respectively.

NDA 2015 Solution View → 76

What is the solution of the differential equation y d x-x d y y^2 =0 ? where c is an arbitrary constant.

NDA 2015 Solution View → 77

What is the solution of the differential equation d x d y + x y -y^2=0 ? where c is an arbitrary constant.

NDA 2015 Solution View → 78

Consider the following statements: 1. The general solution of d y d x =f(x)+x is of the form y=g(x)+c , where c is an arbitrary constant. 2. The degree of ( d y d x )^2=f(x) is 2 .

NDA 2015 Solution View → 79

What is the solution of the differential equation ( d y d x )-a=0 ? where c is an arbitrary constant.

NDA 2015 Solution View → 80

Eliminating the arbitrary constants B and C in the expression y= 2 3 C ( C x-1)^ 3 / 2 + B , we get

NDA 2014 Solution View → 81

What is the degree of the differential equation ( d^3 y d x^3 )^ 3 / 2 = ( d^2 y d x^2 )^2 ?

NDA 2014 Solution View → 82

What is the general solution of the differential equation x d y-y d x=y^2 ? where c is an arbitrary constant

NDA 2014 Solution View → 83

Paragraph : The general solution of the differential equation (x^2+x+1 ) d y+ (y^2+y+1 ) d x=0 is (x+y+1)=A(1+B x+C y+D x y) where B, C and D are constants and A is parameter. Ques

NDA 2014 Solution View → 84

What is the equation of a curve passing through (0,1) and whose differential equation is given by d y=y x d x ?

NDA 2014 Solution View → 85

What is the number of arbitrary constants in the particular solution of differential equation of third order?

NDA 2014 Solution View → 86

Consider the following statements in respect of the differential equation d^2 y d x^2 + ( d y d x )=0 : 1. The degree of the differential equation is not defined. 2. The order of t

NDA 2014 Solution View → 87

What is the solution of the equation ( d y d x )+x=0 ? where c is an arbitrary constant.

NDA 2014 Solution View → 88

What is the solution of d y d x +2 y=1 satisfying y(0)=0 ?

NDA 2014 Solution View → 89

Paragraph : The general solution of the differential equation (x^2+x+1 ) d y+ (y^2+y+1 ) d x=0 is (x+y+1)=A(1+B x+C y+D x y) where B, C and D are constants and A is parameter. Ques

NDA 2014 Solution View → 90

The solution of d y d x =|x| is: where c is an arbitrary constant

NDA 2014 Solution View → 91

Paragraph : The general solution of the differential equation (x^2+x+1 ) d y+ (y^2+y+1 ) d x=0 is (x+y+1)=A(1+B x+C y+D x y) where B, C and D are constants and A is parameter. Ques

NDA 2014 Solution View → 92

What is the order of the differential equation ( d y d x )^2+ d y d x - ^2 y=0 ?

NDA 2013 Solution View → 93

y=2 x+3 x satisfies which of the following differential equations? 1. d^2 y d x^2 +y=0 2. ( d y d x )^2+ d y d x =0 Select the correct answer using the code given below.

NDA 2013 Solution View → 94

The differential equation of all circles whose centres are at the origin is

NDA 2013 Solution View → 95

What is the degree of the differential equation ( d^4 y d x^4 )^ 3 5 -5 d^3 y d x^3 +6 d^2 y d x^2 -8 d y d x +5=0 ?

NDA 2013 Solution View → 96

The general solution of the differential equation ( d y d x )+x=0 is

NDA 2013 Solution View → 97

The general solution of the differential equation x d y d x +y=0 is where c is an orbitrary constant.

NDA 2013 Solution View → 98

The degree and order respectively of the differential equation d y d x = 1 x+y+1 are

NDA 2013 Solution View → 99

The differential equation of the curve y= x is

NDA 2013 Solution View → 100

Consider a differential equation of order m and degree n . Which one of the following pairs is not feasible?

NDA 2012 Solution View → 101

The differential equation y d y d x +x=a where ' a ' is any constant represents :

NDA 2012 Solution View → 102

The differential equation representing the family of curves y=a ( x+ ) is :

NDA 2012 Solution View → 103

What is the general solution of the differential equation x^2 d y+y^2 d x=0 ?

NDA 2012 Solution View → 104

What is the general solution of the differential equation e^x y d x+ (1-e^x ) ^2 y d y=0 ?

NDA 2012 Solution View → 105

For the differential equation ( d y d x )^2-x ( d y d x )+y=0 , which one of the following is not its solution?

NDA 2012 Solution View → 106

What is the solution of the differential equation d y d x + y x =0 ? where c is a constant.

NDA 2012 Solution View → 107

Which of the following differential equations is not linear?

NDA 2012 Solution View → 108

What is the degree of the differential equation d^3 y d x^3 +2 ( d^2 y d x^2 )- d y d x +y=0 ?

NDA 2012 Solution View → 109

What is the degree of the differential equation y=x d y d x + ( d y d x )⁻¹ ?

NDA 2012 Solution View → 110

What is the equation of the curve passing through the point (0, 3 ) satisfying the differential equation x y d x+ x y d y=0 ?

NDA 2011 Solution View → 111

What is the solution of the differential equation d y d x + 1-y^2 1-x^2 =0 ? where c is a constant.

NDA 2011 Solution View → 112

What is the differential equation of all parabolas whose axes are parallel to y -axis? where c is a constant.

NDA 2011 Solution View → 113

What is the degree of the following differential equation? ( d^3 y d x^3 )^ 2 3 +4-3 d^2 y d x^2 +5 d y d x =0

NDA 2011 Solution View → 114

What is the degree of the differential equation ( d^3 y d x^3 )^ 2 3 +4-3 ( d^2 y d x^2 )+5 ( d y d x )=0 ?

NDA 2011 Solution View → 115

If the solution of the differential equation d y d x = a x+3 2 y+f represents a circle, then what is the value of a ?

NDA 2011 Solution View → 116

What does the differential equation y d y d x +x=a (where a is a constant) represent?

NDA 2011 Solution View → 117

What is the general solution of (1+x^x ) y d y=e^x d x ?

NDA 2010 Solution View → 118

Which one of the following is the differential equation to family of circles having centre at the origin?

NDA 2010 Solution View → 119

A particular solution of a differential equation represents

NDA 2010 Solution View → 120

What is the solution of the differential equation a (x d y d x +2 y )=x y d y d x ?

NDA 2010 Solution View →
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