Calculus

Differential Equations

Medium

common

Match List-I with List-II

List-I (Differential Equation) List-II (Degree)
(A) $2(y'')^2 + 3y = 6$ (I) 4
(B) $2y + 5(y')^4 = 7$ (II) 1
(C) $\log x + (y'')^3 = e^x$ (III) 2
(D) $\sqrt{1-2y'} = 5(y'')^{\frac{1}{4}}$ (IV) 3

Choose the correct answer from the options given below:

List-I (Differential Equation)	List-II (Degree)
(A) $2(y'')^2 + 3y = 6$	(I) 4
(B) $2y + 5(y')^4 = 7$	(II) 1
(C) $\log x + (y'')^3 = e^x$	(III) 2
(D) $\sqrt{1-2y'} = 5(y'')^{\frac{1}{4}}$	(IV) 3

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

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

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

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

✅ Correct Option: 4

Degree is the power of the highest-order derivative once the equation is polynomial in derivatives. (A) $(y'')^2$ gives degree 2 (III). (B) highest order is $y'$ with power 4, degree 4 (I). (C) $(y'')^3$ gives degree 3 (IV). (D) squaring twice gives $(1-2y')^2=625\,y''$ , so degree 1 (II).

2026: 29 May Shift 1

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

(where $c$ is an arbitrary constant)

2025: 3 June Shift 1

Consider the differential equation $xdy = (y + 2x^3)dx$ . Then which of the following are TRUE?

(A) It is a homogeneous differential equation.

(B) Product of the order and degree of the differential equation in one.

(D) General solution of the differential equation is $y = x^3 + Cx$ , where C is an arbitary constant.

Choose the correct answer from the options given below:

2022: 7 Aug Shift 2

If curve represented by differential equation $x \frac{dy}{dx} + y = e^x$ passes through (1, 1), then $y(-1)$ is :

2025: 13 May Shift 2

The integrating factor of the differential equation, $x^2 \frac{dy}{dx} + xy = log_e x$ is equal to

2025: 3 June Shift 2

The number of arbitrary constants in the particular solution of a differential equation of order 4 and degree 3 is

2025: 22 May Shift 1

Match List-I with List-II

List-I	List-II
Differential Equation	Degree
(A) $xy\frac{d^2y}{dx^2} + x\left(\frac{dy}{dx}\right)^2 - y\frac{dy}{dx} = 0$	(I) 3
(B) $\frac{d^2y}{dx^2} + \log\left(\frac{dy}{dx}\right) = 0$	(II) 1
(C) $\left(\frac{d^2y}{dx^2}\right)^2 + \left(\frac{dy}{dx}\right)^3 + \frac{dy}{dx} + 1 = 0$	(III) not defined
(D) $2x^2\left(\frac{d^2y}{dx^2}\right)^3 - 5\left(\frac{dy}{dx}\right)^3 + y = 0$	(IV) 2

Choose the correct answer from the options given below:

Solution

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