CUET Mathematics - The integrating factor of the differential equation, x^2 dy/dx + xy = log_e x is equal to | PYQs + Solutions

CUET Mathematics 2025 13 May Shift 2

Calculus

Medium

core

$e^x$

$e^{\frac{x^2}{2}}$

$x$

$log_e x$

✅ 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) $\left(1 + \frac{dy}{dx}\right)^{3/2} = 4\left(\frac{d^2y}{dx^2}\right)^3$	(III) order = 2 and degree = 2
(D) $\frac{d^2y}{dx^2} + 1 = \frac{dy}{dx}$	(IV) order = 2 and degree = 4

Choose the correct answer from the options given below:

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The solution of the differential equation $\frac{dy}{dx} = \frac{x+y}{x-y}$ is

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The product of order and degree of the differential equation $\left(\frac{d^3y}{dx^3}\right)^3 + x^2y\left(\frac{d^2y}{dx^2}\right)^3 = 2x^5$ is:

CUET Mathematics 2025 13 May Shift 2 PYQs