CUET Mathematics - For |x| < 1, if x = (1/a y), then | PYQs + Solutions

CUET Mathematics 2025 15 May Shift 1

Calculus

Hard

core

$(1 - x^2)\frac{d^2y}{dx^2} + x\frac{dy}{dx} - a^2y = 0$

$(1 - x^2)\frac{d^2y}{dx^2} - x\frac{dy}{dx} + a^2y = 0$

$(1 - x^2)\frac{d^2y}{dx^2} - x\frac{dy}{dx} - a^2y = 0$

$(1 - x^2)\frac{d^2y}{dx^2} + x\frac{dy}{dx} + a^2y = 0$

✅ Correct Option: 3

Related questions:

2 June Shift 1

Match List-I with List-II

List-I	List-II
(A) The degree of differential equation $\frac{d^3y}{dx^3} = e^{\frac{dx}{dy}}$	(I) 2
(B) The order of differential equation $\left(\frac{dy}{dx}\right)^3 + \frac{d^3y}{dx^3} = 0$	(II) 4
(C) The sum of order and degree of differential equation $\frac{d}{dx}\left(\frac{d^2y}{dx^2}\right) + \left(\frac{dy}{dx}\right)^2 = x$	(III) not defined
(D) The number of arbitrary constants in the general solution of a differential equation of order 2	(IV) 3

Choose the correct answer from the options given below:

21 May Shift 2

Match List-I with List-II

List-I	List-II
(A) Integrating factor of $xdy - (y + x^2)dx = 0$	(I) $x^2$
(B) Integrating factor of $xdy + (2y + x^2)dx = 0$	(II) $x^3$
(C) Integrating factor of $(3y - x^2)dx + xdy = 0$	(III) $x$
(D) Integrating factor of $(y + 3x^2)dx + xdy = 0$	(IV) $\frac{1}{x}$

Choose the correct answer from the options given below:

3 June Shift 2

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

CUET Mathematics 2025 15 May Shift 1 PYQs