# Solve: $\rm \frac{dy}{dx}$ + 2xy = y

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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.