Calculus

Differential Equations

Easy

common

Match the LIST-I with LIST-II

LIST-I (Differential Equation) LIST-II (Degree of Differential Equation)
A. $\dfrac{d^3y}{dx^3} + \left(\dfrac{d^2y}{dx^2}\right)^2 - \dfrac{dy}{dx} + y = 0$ I. 2
B. $\dfrac{dy}{dx} + \left(\dfrac{d^2y}{dx^2}\right)^4 + 2\left(\dfrac{d^3y}{dx^3}\right)^3 = 0$ II. 4
C. $\left(\dfrac{d^3y}{dx^3}\right)^2 + \left(\dfrac{d^2y}{dx^2}\right)^4 - y = 0$ III. 1
D. $\left(\dfrac{d^2y}{dx^2}\right)^4 + \left(\dfrac{dy}{dx}\right)^3 + y = 0$ IV. 3

Choose the correct answer from the options given below:

LIST-I (Differential Equation)		LIST-II (Degree of Differential Equation)
A. $\dfrac{d^3y}{dx^3} + \left(\dfrac{d^2y}{dx^2}\right)^2 - \dfrac{dy}{dx} + y = 0$		I. 2
B. $\dfrac{dy}{dx} + \left(\dfrac{d^2y}{dx^2}\right)^4 + 2\left(\dfrac{d^3y}{dx^3}\right)^3 = 0$		II. 4
C. $\left(\dfrac{d^3y}{dx^3}\right)^2 + \left(\dfrac{d^2y}{dx^2}\right)^4 - y = 0$		III. 1
D. $\left(\dfrac{d^2y}{dx^2}\right)^4 + \left(\dfrac{dy}{dx}\right)^3 + y = 0$		IV. 3

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

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

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

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

✅ Correct Option: 4

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

A: highest is $y'''$ with power $1$ , so degree $1$ (III).

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

C: $y'''$ has power $2$ , degree $2$ (I).

D: highest is $y''$ with power $4$ , degree $4$ (II).

2025: 27 May Shift 1

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

2025: 13 May Shift 2

The general solution of the differential equation $e^x dy + (y e^x + 2x)dx = 0$ is

2026: 29 May Shift 2

The general solution of the differential equation $x\,dx = (x^2+1)\,dy$ is (where C is an arbitrary constant)

2026: 29 May Shift 2

In reference to the differential equation : $y''+y=(e)^{y'}$ , which of the following statements are correct ?

A. The order of the differential equation is 1.

B. The degree of the differential equation is 1.

C. The order of the differential equation is 2.

D. The degree of the differential equation is not defined.

Choose the correct answer from the options given below:

2026: 22 May Shift 2

Particular solution of the differential equation $dy = e^{2x+y}dx$ , $y(0) = 0$ is:

2025: 21 May Shift 2

Match List-I with List-II

List-I	List-II
(A) Degree of the differential equation $\frac{d^2y}{dx^2} = e^{dy/dx}$ is	(I) 2
(B) Order of the differential equation $(\frac{dy}{dx})^2 + \frac{d^3y}{dx^3} = 0$ is	(II) not defined
(C) Degree of the differential equation $\frac{d^2y}{dx^2} + (\frac{dy}{dx})^2 - 5x^2 = 0$	(III) 3
(D) If p is the order and q is the degree of the differential equation $\frac{dy}{dx} + 3y = e^x$ , then p + q is	(IV) 1

Choose the correct answer from the options given below:

Solution