Calculus

Differential Equations

Medium

common

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:

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

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

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

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

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

✅ Correct Option: 1

Degree is the power of the highest order derivative once the equation is free of radicals and is polynomial in derivatives.

(A) highest order derivative $y''$ has power 2, so degree 2.

(B) $y''$ has power 3, so degree 3.

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

2025: 27 May Shift 1

Match List-I with List-II

List-I	List-II
(A) The degree of the differential equation $\left(\frac{d^2y}{dx^2}\right)^2 + \left(\frac{dy}{dx}\right)^2 = x\sin\left(\frac{dy}{dx}\right)$	(I) 4
(B) The degree of differential equation $\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^{1/4} + x^{1/5} = 0$	(II) 1
(C) The degree of differential equation $\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^3 + 6y^5 = 0$	(III) Not defined
(D) The degree of differential equation $1 + \left(\frac{dy}{dx}\right)^4 = 7\left(\frac{d^2y}{dx^2}\right)^3$	(IV) 3

Choose the correct answer from the options given below:

2026: 18 May Shift 1

Match List-I with List-II

List-I Differential equation	List-II Curve satisfying the differential equation
(A) $\frac{d^2y}{dx^2}+y=0$	(I) $x^2+y^2=C$ : Where C is an arbitrary constant
(B) $\frac{dy}{dx}+y=\frac{x^2+y}{x}$	(II) $3e^{-4y}+4e^{3x}=C$ : Where C is an arbitrary constant
(C) $\frac{dy}{dx}+\frac{x}{y}=0$	(III) $y=\sin x+\cos x+C$ : Where C is an arbitrary constant
(D) $\log(dy/dx)=3x+4y$	(IV) $y=x+Cxe^{-x}$ : Where C is an arbitrary constant

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2025: 19 May Shift 1

Match List-I with List-II

Choose the correct answer from the options given below:

2026: 14 May Shift 2

The solution of the differential equation $\frac{dy}{dx} = x^2 + x + \frac{1}{x}$ is

2026: 14 May Shift 2

Match the LIST-I with LIST-II

LIST-I		LIST-II
A.	The degree of the differential equation $\left(\frac{d^3y}{dx^3}\right)^4+\left(\frac{d^2y}{dx^2}\right)^5+\left(\frac{dy}{dx}\right)+y=0$	I.	0
B.	The order of the differential equation $\left(\frac{d^3y}{dx^3}\right)^4+\left(\frac{d^2y}{dx^2}\right)^5+\left(\frac{dy}{dx}\right)+y^2=0$	II.	4
C.	The number of arbitrary constants in the general solution of a differential equation of second order is	III.	3
D.	The number of arbitrary constants in a particular solution of a differential equation of third order is	IV.	2

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2025: 19 May Shift 1

Solution of the differential equation

$\frac{dy}{dx} = \sqrt{1 + x^2 + y^2 + x^2y^2}$ is : (Here $C$ is an arbitrary constant)

Solution