CUET Mathematics - The differential equation of the family of curves y = Ae^3x + Be^-3 x, where a and are arbitrary constants, is | PYQs + Solutions

CUET Mathematics 2025 22 May Shift 1

Calculus

Medium

applied

$\frac{d^2y}{dx^2} + 9y = 0$

$\frac{d^2y}{dx^2} + 3y = 0$

$\frac{d^2y}{dx^2} = 9y$

$\frac{d^2y}{dx^2} = 3y$

✅ Correct Option: 3

Related questions:

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:

3 June Shift 2

For the differential equation $x\frac{dy}{dx} + 2y = x^2\log_e x$

(A) Integrating factor is $2x$

(B) Integrating factor is $x^2$

(D) General Solution is $y = \frac{x^4}{16}(4\log_e|x| - 1) + C$ Where C is an arbitrary constant.

Choose the correct answer from the options given below:

22 May Shift 2

The solution of the differential equation $\frac{dy}{dx} = (1 + x^2)(1 + y^2)$ is (Here C is an arbitrary constant)

CUET Mathematics 2025 22 May Shift 1 PYQs