\[ x^2 \left (-y'(x)\right )+y''(x)-(x+1)^2 y(x)=0 \] ✓ Mathematica : cpu = 0.836213 (sec), leaf count = 43
\[\left \{\left \{y(x)\to e^{\frac {x^3}{3}+x} \left (c_2 \int _1^x e^{-\frac {1}{3} K[1] \left (K[1]^2+6\right )} \, dK[1]+c_1\right )\right \}\right \}\]
✓ Maple : cpu = 0.22 (sec), leaf count = 50
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\it HeunT} \left ( 0,-3,2\,\sqrt [3]{3},{\frac {{3}^{{\frac {2}{3}}}x}{3}} \right ) {{\rm e}^{-x}}+{\it \_C2}\,{\it HeunT} \left ( 0,3,2\,\sqrt [3]{3},-{\frac {{3}^{{\frac {2}{3}}}x}{3}} \right ) {{\rm e}^{{\frac {x \left ( {x}^{2}+3 \right ) }{3}}}} \right \} \]