CUET Mathematics - For the differential equation xdy/dx + 3y = x^2_e x, which of the following statements are TRUE? (A) Product of order and degree is 1 (B) Integrating factor is x^3 (C) Integrating factor is 3x (D) General solution is y = x^3/36(6_e|x| - 1) + Cx^-3, C is an arbitrary constant. Choose the correct answer from the options given below: | PYQs + Solutions

CUET Mathematics 2025 29 May Shift 2

Calculus

Medium

core

(A), (C) and (D) only

(A) and (B) only

(A) and (D) only

(A), (B) and (D) only

✅ Correct Option: 2

Related questions:

30 May Shift 1

For the differential equation $y\frac{dx}{dx} - (x + 3y^2)dy = 0$ , which of the following statements are true?

(A) It is a linear differential equation

(B) It is a homogenous differential equation

(D) If $y(0) = 1$ , then its particular solution is $x = 3y^2 - 1$

Choose the correct answer from the options given below:

15 May Shift 2

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

15 May Shift 1

Match List-I with List-II

List-I	List-II
(Differential equation)	(Order and Degree)
(A) $\frac{d^3y}{dx^3} + y^2 + e^{dy/dx} = 0$	(I) order = 3, degree = 1
(B) $\left(\frac{d^2y}{dx^2}\right)^3 + \left(\frac{dy}{dx}\right)^2 + \frac{dy}{dx} + 1 = 0$	(II) order = 3, degree not defined
(C) $2x^2\frac{d^2y}{dx^2} - 3\left(\frac{dy}{dx}\right)^2 + y = 0$	(III) order = 2, degree = 3
(D) $\frac{d^3y}{dx^3} + 2\left(\frac{dy}{dx}\right)^2 + \frac{dy}{dx} = 0$	(IV) order = 2, degree = 1

Choose the correct answer from the options given below:

CUET Mathematics 2025 29 May Shift 2 PYQs