Calculus

Differential Equations

Medium

applied

Match List-I with List-II

List-I List-II
Differential equation Order and degree
(A) $y''' + x^2(y'')^3 + y = 0$ (I) $3, 2$
(B) $y''' + y^2 + e^{y'} = 0$ (II) $3, 3$
(C) $(y''')^2 + x^2(y'')^3 + xy = 0$ (III) $3, 1$
(D) $(y''')^3 + x(y'')^2 + y = 0$ (IV) $3, \text{Not defined}$

Choose the correct answer from the options given below:

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

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

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

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

✅ Correct Option: 2

All four have highest derivative $y'''$ , so order 3 throughout; the degree is the power of $y'''$ after clearing radicals.

(A) power 1, degree 1.

(B) $e^{y'}$ is not polynomial in derivatives, so degree is not defined.

(D) power 3, degree 3.

2026: 15 May Shift 1

Match the LIST-I with LIST-II

	LIST-I (Differential equation)		LIST-II (Sum of order and degree)
A.	$(y'')^3 + xy' + 2y = 0$	I.	$6$
B.	$(y'')^2 + (y')^3 + 4y = 0$	II.	$3$
C.	$y'' + (y')^2 + 5y = 0$	III.	$4$
D.	$(y'')^4 + 3x(y')^2 + y = 0$	IV.	$5$

Choose the correct answer from the options given below:

2026: 26 May Shift 2

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:

2025: 22 May Shift 1

The solution of the differential equation $\frac{dy}{dx} - \frac{y}{x} = 2\log_e x$

2026: 29 May Shift 2

The order of the differential equation $\left(\frac{d^3y}{dx^3}\right)^4 + \frac{d^4y}{dx^4} + \log\left(\frac{dy}{dx}\right) = 0$ is

2023: 23 May Shift 3

The general solution of $\frac{dy}{dx} = 1 + x^2 + y^2 + x^2y^2$ is:

(given that $C$ is the constant of integration)

2022: 4 Aug Shift 1

Solution of the differential equation $\frac{dy}{dx} = x + xy - (1 + y)$ is:

Solution