Mathematics - Differential Equation Question with Solution | TestHub

$y+x\frac{dy}{dx}=x^2$

$\frac{dy}{dx}+\frac{y}{x}=x$

$I.F.=e^{\int \frac{1}{x}dx}=x$

Solution of differential equation,

$y·x=\int x·x dx$

$xy=\frac{x^3}{3}+C$

Passes through $\left(-2, 2\right)$, So, 

$-12=-8+3C$

$C=\frac{-4}{3}$

$\therefore 3xy=x^3-4$

i.e $3x·f\left(x\right)=x^3-4$

$x^3-3x f\left(x\right)-4=0$