CUET Mathematics - Consider the differential equation xdy = (x + y) dx. Which of the following are true? (A) It is a homogenous differential equation (B) It is a differential equation of order 2 (C) The general solution of the differential equation contains 2 arbitrary constants (D) Integrating factor of differential equation is 1/x (E) Degree of the differential equation is not defined Choose the correct answer from the options given below: | PYQs + Solutions

CUET Mathematics 2025 15 May Shift 2

Calculus

Medium

common

(A), (B) and (C) only

(A), (D) and (E) only

(A) and (D) only

(B) and (C) only

✅ Correct Option: 3

Related questions:

22 May Shift 1

Which of the following statements is/are true?

(A) $(\tan^{-1} y - x)dy = (1 + y^2)dx$ is a differential equation where variables are separable.

(B) $(1 + x^2)dy + 2xydy = \cot x \ dx (x \neq 0)$ is a first order linear differential equation.

(D) $(xy)dx - (x + y^2)dy = 0$ is a homogeneous differential equation.

Choose the correct answer from the options given below:

22 May Shift 2

Match List-I with List-II

List-I	List-II
Differential Equation	Order and Degree
(A) $\left(\frac{d^2y}{dx^2}\right)^2 = e^x\left(\frac{dy}{dx}\right)^4 + 1 = 0$	(I) order = 1 and degree = 2
(B) $\left(\frac{dy}{dx}\right)^2 + xy = 0$	(II) order = 2 and degree = 1
(C) $\left(1 + \frac{dy}{dx}\right)^{3/2} = 4\left(\frac{d^2y}{dx^2}\right)^2$	(III) order = 2 and degree = 2
(D) $\sqrt\frac{d^2y}{dx^2} + 1 = \frac{dy}{dx}$	(IV) order = 2 and degree = 4

Choose the correct answer from the options given below:

CUET Mathematics 2024 Slot 1

The degree of the differential equation $\left(1-\left(\frac{d y}{d x}\right)^{2}\right)^{\frac{3}{2}}=k \frac{d^{2} y}{d x^{2}}$ is :

CUET Mathematics 2025 15 May Shift 2 PYQs