NDA PYQ Differential Equations - Chapter-wise Questions with Solutions

About Differential Equations PYQs

Differential Equations has 127 previous year questions in the Quantrex Academy NDA Mathematics bank. The 127 questions in this list come from NDA (127), spanning 2010 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

NDA Differential Equations PYQs with Solutions

About Differential Equations PYQs

Questions by year (this list)

Differential Equations questions with solutions

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 ?

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

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 ?

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

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

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

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) ?

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

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

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?

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?

Let y_1(x) and y_2(x) be two solutions of the differential equation (d y)/(d x)=x . If y_1(0)=0 and y_2(0)=4 , then what is the number of points of intersection of curves y_1(x)

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?

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?

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 ?

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

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

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

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?

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

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

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

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

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

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

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

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

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

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

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

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?

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

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

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

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

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

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

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

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

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?

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 ?

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

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

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

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

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

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

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?

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

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

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

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

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

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

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

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 ?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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