The general solution of the differential equation $\frac{dy}{dx}-\frac{y}{x}=x^2$ is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $y=\frac{x^3}{2}+Cx$, where C is a constant
$\frac{dy}{dx}-\frac{y}{x}=x^2$ → eq.
$I.F. = e^{-\int\frac{1}{x}dx}=e^{-\log x}=\frac{1}{x}$
multiplying eq with I.F.
$\int\frac{1}{x}\frac{dy}{dx}-\frac{y}{x}dx=\int xdx$
$⇒\frac{y}{x}=\frac{x^2}{2}+C$
$⇒y=\frac{x^3}{2}+Cx$