\[ \left (x^2+x-1\right ) y'(x)+(x+1)^2 y''(x)+(-x-2) y(x)=0 \] ✓ Mathematica : cpu = 0.241553 (sec), leaf count = 88
DSolve[(-2 - x)*y[x] + (-1 + x + x^2)*Derivative[1][y][x] + (1 + x)^2*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to c_2 e^{-x} \int _1^x\exp \left (-\frac {K[1]^2}{K[1]+1}-\frac {K[1]}{K[1]+1}+2 K[1]-\frac {1}{K[1]+1}\right ) (K[1]+1)^{\frac {K[1]}{K[1]+1}+\frac {1}{K[1]+1}}dK[1]+c_1 e^{-x}\right \}\right \}\] ✓ Maple : cpu = 0.365 (sec), leaf count = 53
dsolve((1+x)^2*diff(diff(y(x),x),x)+(x^2+x-1)*diff(y(x),x)-(x+2)*y(x)=0,y(x))
\[y \left (x \right ) = \left (1+x \right ) \left (c_{2} \operatorname {HeunD}\left (-4, 4, -8, 12, \frac {x}{x +2}\right ) {\mathrm e}^{\frac {x -1}{2 x +2}}+c_{1} {\mathrm e}^{-x} \operatorname {HeunD}\left (4, 4, -8, 12, \frac {x}{x +2}\right )\right )\]