\[ x y''(x)-x y'(x)-y(x)-e^x x (x+1)=0 \] ✓ Mathematica : cpu = 0.0557073 (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 = 0.07 (sec), leaf count = 33
\[ \left \{ y \left ( x \right ) ={{\rm e}^{x}} \left ( {\it \_C1}\,x{\it Ei} \left ( 1,x \right ) -{{\rm e}^{-x}}{\it \_C1}-x\ln \left ( x \right ) +{\it \_C2}\,x+{x}^{2}-1 \right ) \right \} \]