Solve the following differential equation: x (dy)/(dx) + 2y = x² log x

$\frac{dy}{dx} + \frac{2}{x}y = x\log x$, linear with $P = \frac{2}{x}$. I.F. $= e^{\int\frac{2}{x}dx} = x^2$. $yx^2 = \int x^3\log x\,dx = \frac{x^4}{4}\log x - \int\frac{x^3}{4}dx = \frac{x^4}{4}\log x - \frac{x^4}{16} + C$. Hence $y = \frac{x^2}{4}\log x - \frac{x^2}{16} + \frac{C}{x^2}$.