\[ \boxed { \left ( 1+x \right ) ^{2}{\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) + \left ( {x}^{2}+x-1 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( x+2 \right ) y \left ( x \right ) =0} \]
Mathematica: cpu = 38.898939 (sec), leaf count = 87 \[ \left \{\left \{y(x)\to c_2 e^{-x} \int _1^x (K[1]+1)^{\frac {K[1]}{K[1]+1}+\frac {1}{K[1]+1}} \exp \left (-\frac {K[1]^2}{K[1]+1}-\frac {K[1]}{K[1]+1}+2 K[1]-\frac {1}{K[1]+1}\right ) \, dK[1]+c_1 e^{-x}\right \}\right \} \]
Maple: cpu = 0.171 (sec), leaf count = 55 \[ \left \{ y \left ( x \right ) ={\it \_C1}\,{{\rm e}^{-x}}{\it HeunD} \left ( 4,4,-8,12,{\frac {x}{x+2}} \right ) \left ( 1+x \right ) +{\it \_C2}\,{\it HeunD} \left ( -4,4,-8,12,{\frac {x}{x+2}} \right ) \left ( 1+x \right ) {{\rm e}^{{\frac {x-1}{2\,x+2}}}} \right \} \]