\[ x^2 \left (-y'(x)\right )+y''(x)-(x+1)^2 y(x)=0 \] ✓ Mathematica : cpu = 0.0487047 (sec), leaf count = 56
\[\left \{\left \{y(x)\to c_2 e^{\frac {x^3}{3}+x} \int _1^xe^{-\frac {1}{3} K[1]^3-2 K[1]}dK[1]+c_1 e^{\frac {x^3}{3}+x}\right \}\right \}\] ✓ Maple : cpu = 0.866 (sec), leaf count = 50
\[ \left \{ y \left ( x \right ) ={\it \_C1}\,{\it HeunT} \left ( 0,-3,2\,\sqrt [3]{3},{\frac {{3}^{{\frac {2}{3}}}x}{3}} \right ) {{\rm e}^{-x}}+{\it \_C2}\,{\it HeunT} \left ( 0,3,2\,\sqrt [3]{3},-{\frac {{3}^{{\frac {2}{3}}}x}{3}} \right ) {{\rm e}^{{\frac {x \left ( {x}^{2}+3 \right ) }{3}}}} \right \} \]