Calculus

Differential Equations

Medium

applied

Match the LIST-I with LIST-II

[ $a$ is an arbitrary constant]

LIST-I
Differential Equation LIST-II
Family of curves
A. $x\,dy - y\,dx = 0$ I. $x^2 + y^2 = a^2$
B. $2y\,dx - x\,dy = 0$ II. $y = ax$
C. $x\,dx + y\,dy = 0$ III. $y^2 = 16x + a$
D. $y\,dy - 8\,dx = 0$ IV. $x^2 = ay$

Choose the correct answer from the options given below:

	LIST-I Differential Equation		LIST-II Family of curves
A.	$x\,dy - y\,dx = 0$	I.	$x^2 + y^2 = a^2$
B.	$2y\,dx - x\,dy = 0$	II.	$y = ax$
C.	$x\,dx + y\,dy = 0$	III.	$y^2 = 16x + a$
D.	$y\,dy - 8\,dx = 0$	IV.	$x^2 = ay$

A-III, B-I, C-IV, D-II

A-II, B-IV, C-I, D-III

A-IV, B-II, C-III, D-I

A-I, B-III, C-II, D-IV

✅ Correct Option: 2

$x\,dy = y\,dx$ integrates to $y = ax$ . From $2y\,dx = x\,dy$ we get $y = kx^2$ , i.e. $x^2 = ay$ . Next $x\,dx+y\,dy = 0$ gives $x^2+y^2 = a^2$ , and $y\,dy = 8\,dx$ gives $y^2 = 16x+a$ .

2025: 14 May Shift 2

For the differential equation $(x + y)dy + (x - y)dx = 0$ , which of the following is/are correct?

(A) Differential equation is homogeneous

(B) Order of differential equation is 1

(D) Degree of the equation is not defined

Choose the correct answer from the options given below:

2022: 16 July Shift 2

Match List I with List II.

List I	List II
A. $\frac{d^2y}{dx^2} + \frac{dy}{dx} = 0$	I. order 3, degree 1
B. $\left(\frac{d^2y}{dx^2}\right)^2 = 0$	II. order 2, degree 2
C. $\frac{d^3y}{dx^3} + \frac{d^2y}{dx^2} + y = 0$	III. order 2, degree 1
D. $\sin\left(\frac{dy}{dx}\right) + 5y = 0$	IV. order 1, degree is not defined

Choose the correct answer from the options given below:

2026: 29 May Shift 1

The general solution of the differential equation $\dfrac{dy}{dx}=2^{-y}$ is:

(where $c$ is an arbitrary constant)

2026: 19 May Shift 1

The general solution of the differential equation $\frac{dy}{dx} + y\cot x = 2\cos x$ is (Where C is an arbitrary constant)

2026: 29 May Shift 1

Match List-I with List-II

List-I (Differential Equation)	List-II (Degree)
(A) $\left(\dfrac{dy}{dx}\right)^3+\left(\dfrac{d^2y}{dx^2}\right)^2=0$	(I) Not defined
(B) $\left(\dfrac{d^2y}{dx^2}\right)^3+\left(\dfrac{dy}{dx}\right)^2+1=0$	(II) 2
(C) $\sqrt{1+\dfrac{d^2y}{dx^2}}=\dfrac{dy}{dx}+x$	(III) 1
(D) $\dfrac{d^2y}{dx^2}+e^{\frac{dy}{dx}}=0$	(IV) 3

Choose the correct answer from the options given below:

2022: 16 July Shift 2

Integrating factor of the differential equation $\frac{dy}{dx} - \frac{1}{x} y = 1$ is:

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)