Solution of the differential equation dy/dx = x + xy - (1 + y) is: Option 1: |y+1| = Ce^x^2/2 - x Option 2: |y+1| = Ce^x - x^2/2 Option 3: y = x^2/2 - x^2 y^2/2 - x + y^2/2 + C Option 4: y^2/2 + y = x^2/2 - x + C

The answer is '|y+1| = Ce^x^2/2 - x'. View full solution:

CUET Mathematics - Solution of the differential equation dy/dx = x + xy - (1 + y) is: | PYQs + Solutions

CUET Mathematics 2022 4 Aug Shift 1

Calculus

Medium

$|y+1| = Ce^{\frac{x^2}{2} - x}$

$|y+1| = Ce^{x - \frac{x^2}{2}}$

$y = \frac{x^2}{2} - \frac{x^2 y^2}{2} - x + \frac{y^2}{2} + C$

$\frac{y^2}{2} + y = \frac{x^2}{2} - x + C$

✅ Correct Option: 1

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