Calculus

Differential Equations

Medium

common

Match the LIST-I with LIST-II

LIST-I
Differential equation LIST-II
Order and Degree
A. $\left(\dfrac{dy}{dx}\right)^2 + 3y\left(\dfrac{d^2y}{dx^2}\right) = 0$ I. $1,1$
B. $\sqrt{1-\left(\dfrac{dy}{dx}\right)^2} = a\left(\dfrac{d^2y}{dx^2}\right)^{1/3}$ II. $1,2$
C. $y = \dfrac{dy}{dx} + \dfrac{5}{(dy/dx)}$ III. $2,1$
D. $\sqrt{1-y^2}\,dx + \sqrt{1-x^2}\,dy = 0$ IV. $2,2$

Choose the correct answer from the options given below:

	LIST-I Differential equation		LIST-II Order and Degree
A.	$\left(\dfrac{dy}{dx}\right)^2 + 3y\left(\dfrac{d^2y}{dx^2}\right) = 0$	I.	$1,1$
B.	$\sqrt{1-\left(\dfrac{dy}{dx}\right)^2} = a\left(\dfrac{d^2y}{dx^2}\right)^{1/3}$	II.	$1,2$
C.	$y = \dfrac{dy}{dx} + \dfrac{5}{(dy/dx)}$	III.	$2,1$
D.	$\sqrt{1-y^2}\,dx + \sqrt{1-x^2}\,dy = 0$	IV.	$2,2$

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

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

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

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

✅ Correct Option: 4

A: highest derivative $\dfrac{d^2y}{dx^2}$ appears to power 1, so order 2, degree 1 (III).

B: cube then square to clear radicals, giving $(1-(y')^2)^3 = a^6(y'')^2$ , so order 2, degree 2 (IV).

C: multiply by $y'$ to get $yy' = (y')^2+5$ , so order 1, degree 2 (II).

D: only first order differentials, degree 1 (I).

2025: 15 May Shift 1

Let $y(x) = a(x + 1) \log(x + 1) + bx + 5$ be the solution of the differential equation e $^\frac{dy}{dx} = x + 1_{;}y(0) = 5$ , then the value of $(a + b)$ is:

2026: 21 May Shift 2

The general solution of the differential equation $(y-x)dy + (x+y)dx = 0$ is: (where C is arbitrary constant)

2026: 15 May Shift 1

The solution of the differential equation $\dfrac{dy}{dx} = \dfrac{x^2+xy+y^2}{x^2}$ for $x>0, y>0$ at $x=1, y=2$ is

2026: 29 May Shift 1

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

(where C is an arbitrary constant)

2026: 31 May Shift 2

General solution of the differential equation $\dfrac{dy}{dx} = e^{ax+by}$ is: (where C is an arbitrary constant)

2026: 19 May Shift 1

Match List-I with List-II

List-I (Differential equation)	List-II (The sum of degree and order of the differential equation)
(A) $x\frac{d^2y}{dx^2} = \left(1+\left(\frac{dy}{dx}\right)^2\right)^{\frac{1}{3}}$	(I) 2
(B) $x\frac{d^2y}{dx^2} = \left(2-\frac{dy}{dx}\right)^{\frac{1}{7}}$	(II) 9
(C) $3+\frac{dy}{dx} = y+\frac{d^3y}{dx^3}$	(III) 4
(D) $\frac{dy}{dx} = x+3$	(IV) 5

Choose the correct answer from the options given below:

Solution

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