Correct Answer - Option 3 : log y = x - x
2 + 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.