2.1109   ODE No. 1109

\[ x y''(x)-x y'(x)-y(x)-e^x x (x+1)=0 \]

✓ Mathematica : cpu = 0.172288 (sec), leaf count = 45

DSolve[-(E^x*x*(1 + x)) - y[x] - x*Derivative[1][y][x] + x*Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_2 \left (-e^x x \text {Ei}(-x)-1\right )+e^x \left (x^2+x-x \log (-x)-1\right )+c_1 e^x x\right \}\right \}\]

✓ Maple : cpu = 0.059 (sec), leaf count = 33

dsolve(x*diff(diff(y(x),x),x)-x*diff(y(x),x)-y(x)-x*(1+x)*exp(x)=0,y(x))
 

\[y \left (x \right ) = {\mathrm e}^{x} \left (-x c_{1} \operatorname {Ei}_{1}\left (x \right )+x^{2}+c_{2} x -x \ln \left (x \right )+{\mathrm e}^{-x} c_{1} -1\right )\]