\[ \left (x^2+x-1\right ) y'(x)+(x+1)^2 y''(x)-(x+2) y(x)=0 \] ✓ Mathematica : cpu = 0.26803 (sec), leaf count = 88
\[\left \{\left \{y(x)\to c_2 e^{-x} \int _1^x\exp \left (-\frac {K[1]^2}{K[1]+1}-\frac {K[1]}{K[1]+1}+2 K[1]-\frac {1}{K[1]+1}\right ) (K[1]+1)^{\frac {K[1]}{K[1]+1}+\frac {1}{K[1]+1}}dK[1]+c_1 e^{-x}\right \}\right \}\] ✓ Maple : cpu = 1.148 (sec), leaf count = 53
\[ \left \{ y \left ( x \right ) = \left ( 1+x \right ) \left ( {\it \_C1}\,{{\rm e}^{-x}}{\it HeunD} \left ( 4,4,-8,12,{\frac {x}{x+2}} \right ) +{\it \_C2}\,{\it HeunD} \left ( -4,4,-8,12,{\frac {x}{x+2}} \right ) {{\rm e}^{{\frac {x-1}{2\,x+2}}}} \right ) \right \} \]