General solution of the differential equation dy/dx = e^x^2/2 + xy is Option 1: y = c e^x^2/2, where c is constant of integration. Option 2: y = c e^-x^2/2, where c is constant of integration. Option 3: y = (x + c) e^x^2/2, where c is constant of integration. Option 4: y = (x + c) e^-x^2/2, where c is constant of integration.

The answer is 'y = (x + c) e^x^2/2, where c is constant of integration.'. View full solution:

CUET Mathematics - General solution of the differential equation dy/dx = e^x^2/2 + 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

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(D) Integrating factor of $(y + 3x^2)dx + xdy = 0$	(IV) $\frac{1}{x}$

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