\[ x y''(x)-x y'(x)-y(x)-e^x x (x+1)=0 \] ✓ Mathematica : cpu = 0.0560817 (sec), leaf count = 45
\[\left \{\left \{y(x)\to c_2 \left (-e^x x \text {Ei}(-x)-1\right )+c_1 e^x x+e^x \left (x^2+x-x \log (-x)-1\right )\right \}\right \}\]
✓ Maple : cpu = 0.027 (sec), leaf count = 40
\[ \left \{ y \left ( x \right ) = \left ( -{\it Ei} \left ( 1,x \right ) x+{{\rm e}^{-x}} \right ) {{\rm e}^{x}}{\it \_C1}+{{\rm e}^{x}}{\it \_C2}\,x- \left ( x\ln \left ( x \right ) -{x}^{2}+1 \right ) {{\rm e}^{x}} \right \} \]