The differential equation $x\frac{dy}{dx} -y =x^2$, has the general solution
Answer & explanation
Correct answer: option 2
The correct answer is option (2) : $2y-x^3=Cx$
We have,
$\frac{dy}{dx} + \left(-\frac{1}{x}\right) y = x^2$
It is a linear differential equation with integrating factor
$I.F.=e^{∫-\frac{1}{x}dx}=e^{-log\, x}=\frac{1}{x}$
Multiplying (i) by $\frac{1}{x}$ and integrating, we get
$\frac{y}{x}=\frac{x^2}{2}+C$ or , $2y-x^3=2Cx$