CUET Mathematics - The general solution of the differential equation (1 + e^x)dy + ye^x dx = 0, where y > 0, is | PYQs + Solutions

CUET Mathematics 2025 15 May Shift 1

Calculus

Medium

common

$y = C(1 + e^x)$ , C is an arbitary constant

$\frac{C}{e^x} = \frac{y}{1 + e^x}$ , C is an arbitary constant

$C = y(1 + e^x)$ , C is an arbitary constant

$y = \frac{Ce^x}{1 + e^x}$ , C is an arbitary constant

✅ Correct Option: 3

Related questions:

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The general solution of the differential equation $(x^2 - yx^2)dy + (y^2 + x^2y^2)dx = 0$ is:

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A integrating factor of the differential equation $\frac{dy}{dx} + \frac{y}{x} = \frac{1}{x^2}$ , $(x > 0)$ is equal to

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Match List-I with List-II

List-I	List-II
(A) The degree of the differential equation $\left(\frac{d^2y}{dx^2}\right)^2 + \left(\frac{dy}{dx}\right)^3 = x\sin\left(\frac{dy}{dx}\right)$	(I) 4
(B) The degree of differential equation $\frac{d^3y}{dx^3} + \left(\frac{dy}{dx}\right)^{1/3} + x^{1/5} = 0$	(II) 1
(C) The degree of differential equation $\frac{d^2y}{dx^2} + x\left(\frac{dy}{dx}\right)^3 + 6y^5 = 0$	(III) Not defined
(D) The degree of differential equation $1 + \left(\frac{dy}{dx}\right)^3 = 7\left(\frac{d^2y}{dx^2}\right)^3$	(IV) 3

Choose the correct answer from the options given below:

CUET Mathematics 2025 15 May Shift 1 PYQs