Solve {l}{x^{2}d^2y/dx^2+xdy/dx-y=x^2logx}{tx=e^2-0}

$$\left. \begin{array} { l } { x ^ { 2 } \frac { d ^ { 2 } y } { d x ^ { 2 } } + x \frac { d y } { d x } - y = x ^ { 2 } \log x } \\ { t x = e ^ { 2 } - 0 } \end{array} \right.$$

Solve for x, y (complex solution)

$$x=\frac{e^{2}}{t}$$

$$y=-\frac{e^{4}\log(e)\left(\ln(\frac{1}{t})+2\right)}{t^{2}}$$

$$t\neq 0$$

Solve for x, y

$$x=\frac{e^{2}}{t}$$

$$y=-\frac{e^{4}\log(e)\left(-\ln(t)+2\right)}{t^{2}}$$

$$t>0$$