The general solution of the differential equation dy/dx=e^2x-y+xe^-y is: Option 1: 2e^-y=e^2x+x+C: where C is an arbitrary constant Option 2: 2e^y=e^2x+x^2+C: where C is an arbitrary constant Option 3: 2e^-y=e^2x+x^2+C: where C is an arbitrary constant Option 4: 2e^y=e^2x+x+C: where C is an arbitrary constant

The answer is '2e^y=e^2x+x^2+C: where C is an arbitrary constant'. View full solution:

CUET Mathematics - The general solution of the differential equation dy/dx=e^2x-y+xe^-y is: | PYQs + Solutions

CUET Mathematics 2026 22nd May Shift 1

Calculus

Easy

common

$2e^{-y}=e^{2x}+x+C$ : where $C$ is an arbitrary constant

$2e^{y}=e^{2x}+x^2+C$ : where $C$ is an arbitrary constant

$2e^{-y}=e^{2x}+x^2+C$ : where $C$ is an arbitrary constant

$2e^{y}=e^{2x}+x+C$ : where $C$ is an arbitrary constant

✅ Correct Option: 2

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Particular solution of the differential equation $dy + 2xy^2 dx = 0$ , given that $y=1$ , when $x=0$ , is

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Match the LIST-I with LIST-II

LIST-I Differential equation	LIST-II Integrating factor of the differential equation
A. $\dfrac{dy}{dx} + 2y = xe^{4x}$	I. $\dfrac{1}{x}$
B. $2x\dfrac{dy}{dx} + y = 6x^3$	II. $\dfrac{1}{y}$
C. $ydx - xdy + (\log_e x)dx = 0$	III. $e^{2x}$
D. $ydx - (x+2y^2)dy = 0$	IV. $\sqrt{x}$

Choose the correct answer from the options given below: