CUET Mathematics - General solution of the differential equation dy/dx = e^x/2 + xy is | PYQs + Solutions

CUET Mathematics 2025 14 May Shift 2

Calculus

Medium

core

$y = c e^{\frac{x^2}{2}}$ , where $c$ is constant of integration.

$y = c e^{-\frac{x^2}{2}}$ , where $c$ is constant of integration.

$y = (x + c) e^{\frac{x^2}{2}}$ , where $c$ is constant of integration.

$y = (x + c) e^{-\frac{x^2}{2}}$ , where $c$ is constant of integration.

✅ 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:

26 May Shift 2

The particular solution of the differential equation $\frac{dy}{dx} = e^{x/2} + xy$ , when $x = 0$ , $y = 1$ , is

19 May Shift 1

If the slope of the tangent to the curve $y = x(x)$ at any point $(x, y)$ is $\frac{2y}{x}$ and the curve passes through the point $\left(\frac{1}{9}, 1\right)$ , then equation of curve is

CUET Mathematics 2025 14 May Shift 2 PYQs

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