Question

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

Answer 1

$x\frac{dy}{dx}+2x=\log x\frac{dy}{dx}+2=\frac{\log x}{x}\frac{dy}{dx}=\frac{\log x}{x}-2y=\int (\frac{\log x}{x}-2)dxy=\frac{(\log x{)}^2}{2}-2x+c$