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Solve: \(\rm \frac{dy}{dx}\) + 2xy = y
1. log y = x + x2 + C
2. log y = x2 + C
3. log y = x - x2 + C
4. None of these.

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Correct Answer - Option 3 : log y = x - x2 + C

Calculation:

The given differential equation \(\rm \frac{dy}{dx}\) + 2xy = y, is in the variable separable form.

Separating the variables, we get:

\(\rm \frac{dy}{dx}\) = y(1 - 2x)

⇒ \(\rm \frac{1}{y}\ dy\) = (1 - 2x) dx

Integrating both sides, we get:

⇒ ∫\(\rm \frac{1}{y}\ dy\) = ∫(1 - 2x) dx

⇒ log y = x - x2 + C.

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