\[ d y(x)^{1-a}+a y'(x)^2+b y(x) y'(x)+c y(x)^2+y(x) y''(x)=0 \] ✓ Mathematica : cpu = 1.70501 (sec), leaf count = 396
\[\left \{\left \{y(x)\to \left (-\frac {\exp \left (-\frac {x \left (b \sqrt {b^2-4 (a+1) c}-2 (a+1) c+b^2\right )}{\sqrt {b^2-4 (a+1) c}+b}\right ) \left (b^2 \left (d e^{\frac {1}{2} x \left (\sqrt {b^2-4 (a+1) c}+b\right )}-c c_2 \exp \left (\frac {x \left (b \sqrt {b^2-4 (a+1) c}-4 (a+1) c+b^2\right )}{\sqrt {b^2-4 (a+1) c}+b}\right )\right )+(a+1) c \left (-4 d e^{\frac {1}{2} x \left (\sqrt {b^2-4 (a+1) c}+b\right )}+4 c c_2 \exp \left (\frac {x \left (b \sqrt {b^2-4 (a+1) c}-4 (a+1) c+b^2\right )}{\sqrt {b^2-4 (a+1) c}+b}\right )-c_1 \sqrt {b^2-4 (a+1) c}\right )+b d \sqrt {b^2-4 (a+1) c} e^{\frac {1}{2} x \left (\sqrt {b^2-4 (a+1) c}+b\right )}-b c \left (c_2 \sqrt {b^2-4 (a+1) c} \exp \left (\frac {x \left (b \sqrt {b^2-4 (a+1) c}-4 (a+1) c+b^2\right )}{\sqrt {b^2-4 (a+1) c}+b}\right )+(a+1) c_1\right )\right )}{c \left (b \sqrt {b^2-4 (a+1) c}-4 (a+1) c+b^2\right )}\right ){}^{\frac {1}{a+1}}\right \}\right \}\]
✓ Maple : cpu = 0.356 (sec), leaf count = 133
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-{\frac {x}{2\,a+2}\sqrt { \left ( -4\,a-4 \right ) c+{b}^{2}}}}}{{\rm e}^{-{\frac {bx}{2\,a+2}}}} \left ( {( \left ( -4\,a-4 \right ) {c}^{3}+{b}^{2}{c}^{2}) \left ( d{{\rm e}^{{\frac {x}{2} \left ( b+\sqrt { \left ( -4\,a-4 \right ) c+{b}^{2}} \right ) }}}\sqrt { \left ( -4\,a-4 \right ) c+{b}^{2}}+ \left ( a+1 \right ) c \left ( {{\rm e}^{x\sqrt { \left ( -4\,a-4 \right ) c+{b}^{2}}}}{\it \_C1}-{\it \_C2} \right ) \right ) ^{-2}} \right ) ^{- \left ( 2\,a+2 \right ) ^{-1}} \right \} \]