\[ \boxed { {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) -{x}^{2}{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( 1+x \right ) ^{2}y \left ( x \right ) =0} \]
Mathematica: cpu = 0.879612 (sec), leaf count = 55 \[ \left \{\left \{y(x)\to c_2 e^{\frac {x^3}{3}+x} \int _1^x e^{-\frac {1}{3} K[1]^3-2 K[1]} \, dK[1]+c_1 e^{\frac {x^3}{3}+x}\right \}\right \} \]
Maple: cpu = 0.110 (sec), leaf count = 50 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\it HeunT} \left ( 0,-3,2\, \sqrt [3]{3},{\frac {{3}^{{\frac {2}{3}}}x}{3}} \right ) {{\rm e}^{-x}} +{\it \_C2}\,{\it HeunT} \left ( 0,3,2\,\sqrt [3]{3},-{\frac {{3}^{{ \frac {2}{3}}}x}{3}} \right ) {{\rm e}^{{\frac {x \left ( {x}^{2}+3 \right ) }{3}}}} \right \} \]