CUET Mathematics - The differential equation representing the curve y = e^2x(a + bx), where a, b are arbitrary constants is | PYQs + Solutions

CUET Mathematics 2025 21 May Shift 1

Calculus

Medium

applied

$\frac{d^2y}{dx^2} + 4\frac{dy}{dx} + 4y = 0$

$\frac{d^2y}{dx^2} - 4\frac{dy}{dx} - 4y = 0$

$\frac{d^2y}{dx^2} + 4\frac{dy}{dx} + 4y = 0$

$\frac{d^2y}{dx^2} + 4\frac{dy}{dx} - 4y = 0$

✅ Correct Option: 3

Related questions:

26 May Shift 2

Match List-I with List-II

List-I	List-II
Differential Equations	Order and degree
(A) $ydx + x\log(y/x)dy - 2xdy = 0$	(I) Order : 2, degree:1
(B) $\left(\frac{d^3y}{dx^3}\right)^2 + 3\frac{d^2y}{dx^2} + 2\left(\frac{dy}{dx}\right)^4 = y^2$	(II) Order :1, degree:1
(C) $\frac{dy}{dx} + \log\left(\frac{dy}{dx}\right) + x = y$	(III) Order : 3, degree:2
(D) $\left(\frac{ds}{dt}\right)^4 + 2s\frac{d^2s}{dt^2} = 0$	(IV) Order : 1, degree: Not defined

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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

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14 May Shift 1

The integrating factor of the differential equation $(x log_e x)\frac{dy}{dx} + y = 2log_e x$ is

CUET Mathematics 2025 21 May Shift 1 PYQs