Calculus

Differential Equations

Easy

common

Match the LIST-I with LIST-II

LIST-I
Differential equation LIST-II
Sum of the order and the degree of the differential equation
A. $\dfrac{d}{dx}\left(\dfrac{dy}{dx}\right) = 1$ I. $2$
B. $4 + \left(\dfrac{dy}{dx}\right)^4 = 7\left(\dfrac{d^2y}{dx^2}\right)^3$ II. $3$
C. $x^3\left(\dfrac{d^2y}{dx^2}\right)^2 + x\left(\dfrac{dy}{dx}\right)^4 + 1 = 0$ III. $5$
D. $\dfrac{dy}{dx} = x^4 e^{-3y}$ IV. $4$

Choose the correct answer from the options given below:

	LIST-I Differential equation		LIST-II Sum of the order and the degree of the differential equation
A.	$\dfrac{d}{dx}\left(\dfrac{dy}{dx}\right) = 1$	I.	$2$
B.	$4 + \left(\dfrac{dy}{dx}\right)^4 = 7\left(\dfrac{d^2y}{dx^2}\right)^3$	II.	$3$
C.	$x^3\left(\dfrac{d^2y}{dx^2}\right)^2 + x\left(\dfrac{dy}{dx}\right)^4 + 1 = 0$	III.	$5$
D.	$\dfrac{dy}{dx} = x^4 e^{-3y}$	IV.	$4$

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

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

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

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

✅ Correct Option: 1

A reduces to $\frac{d^2y}{dx^2}=1$ : order 2, degree 1, sum 3. B: order 2, degree 3, sum 5. C: order 2, degree 2, sum 4. D: order 1, degree 1, sum 2.

2025: 14 May Shift 2

Match List-I with List-II

List-I	List-II
Differential Equations	Order and degree
(A) $\frac{dy}{dx} + e^y = 0$	(I) order 2, degree not defined
(B) $\frac{d^2y}{dx^2} = \left[1 + \left(\frac{dy}{dx}\right)^2\right]^{3/2}$	(II) order 2, degree 1
(C) $\left(\frac{d^2y}{dx^2}\right)^2 + e^{(\frac{dy}{dx})} = 0$	(III) order 1, degree 1
(D) $\frac{d^2y}{dx^2} + x\frac{dy}{dx} - 2y = logx; x > 0$	(IV) order 2, degree 2

Choose the correct answer from the options given below:

2025: 21 May Shift 2

The solution of the differential equation $(x + 1)\frac{dy}{dx} + 1 - 2e^{-y} = 0$ , $y(0) = 0$ is

2022: 23 Aug Shift 1

The solution of differential equation $y(1 - x^2)\frac{dy}{dx} = x(1 + y^2)$ is :

2023: 23 May Shift 3

In the context of differential equation

Match List I with List II

LIST I	LIST II
A. $\frac{dy}{dx} = \frac{1+y^2}{1+x^2}$	I. Not a differential equation
B. $x^2 \frac{dy}{dx} = x^2 - 2y^2 + xy$	II. Linear first order
C. $\sin x + y = \cos(x+y)$	III. Variable separable
D. $(x+y)\frac{dy}{dx} = 1$	IV. Homogenous

Choose the correct answer from the options given below:

2025: 27 May Shift 1

The particular solution of the differential equation $\frac{dy}{dx} + \frac{3y}{x} = 0$ , $y(1) = 1$ is

2026: 26 May Shift 2

If $\dfrac{dy}{dx} = e^{x-y} + x^2e^{-y}$ , then the solution of the differential equation will be:-

Solution