\[ d y(x)^{1-a}+a y'(x)^2+b y(x) y'(x)+c y(x)^2+y(x) y''(x)=0 \] ✓ Mathematica : cpu = 1.17329 (sec), leaf count = 744
\[\left \{\left \{y(x)\to \left (-\frac {a d \exp \left (\frac {1}{2} x \left (\sqrt {-4 a c+b^2-4 c}+b\right )-\frac {x \left (b \sqrt {-4 a c+b^2-4 c}-4 (a+1) c+b^2\right )}{\sqrt {-4 a c+b^2-4 c}+b}-\frac {2 (a+1) c x}{\sqrt {-4 a c+b^2-4 c}+b}\right )}{(a+1) c}-\frac {d \exp \left (\frac {1}{2} x \left (\sqrt {-4 a c+b^2-4 c}+b\right )-\frac {x \left (b \sqrt {-4 a c+b^2-4 c}-4 (a+1) c+b^2\right )}{\sqrt {-4 a c+b^2-4 c}+b}-\frac {2 (a+1) c x}{\sqrt {-4 a c+b^2-4 c}+b}\right )}{(a+1) c}+\frac {a b c_1 \exp \left (-\frac {x \left (b \sqrt {-4 a c+b^2-4 c}-4 (a+1) c+b^2\right )}{\sqrt {-4 a c+b^2-4 c}+b}-\frac {2 (a+1) c x}{\sqrt {-4 a c+b^2-4 c}+b}\right )}{b \sqrt {-4 a c+b^2-4 c}-4 a c+b^2-4 c}+\frac {b c_1 \exp \left (-\frac {x \left (b \sqrt {-4 a c+b^2-4 c}-4 (a+1) c+b^2\right )}{\sqrt {-4 a c+b^2-4 c}+b}-\frac {2 (a+1) c x}{\sqrt {-4 a c+b^2-4 c}+b}\right )}{b \sqrt {-4 a c+b^2-4 c}-4 a c+b^2-4 c}+\frac {a c_1 \sqrt {-4 a c+b^2-4 c} \exp \left (-\frac {x \left (b \sqrt {-4 a c+b^2-4 c}-4 (a+1) c+b^2\right )}{\sqrt {-4 a c+b^2-4 c}+b}-\frac {2 (a+1) c x}{\sqrt {-4 a c+b^2-4 c}+b}\right )}{b \sqrt {-4 a c+b^2-4 c}-4 a c+b^2-4 c}+\frac {c_1 \sqrt {-4 a c+b^2-4 c} \exp \left (-\frac {x \left (b \sqrt {-4 a c+b^2-4 c}-4 (a+1) c+b^2\right )}{\sqrt {-4 a c+b^2-4 c}+b}-\frac {2 (a+1) c x}{\sqrt {-4 a c+b^2-4 c}+b}\right )}{b \sqrt {-4 a c+b^2-4 c}-4 a c+b^2-4 c}+c_2 e^{-\frac {2 (a+1) c x}{\sqrt {-4 a c+b^2-4 c}+b}}\right ){}^{\frac {1}{a+1}}\right \}\right \}\] ✓ Maple : cpu = 0.972 (sec), leaf count = 133
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-{\frac {x}{2\,a+2}\sqrt { \left ( -4\,a-4 \right ) c+{b}^{2}}}}}{{\rm e}^{-{\frac {bx}{2\,a+2}}}} \left ( {( \left ( -4\,a-4 \right ) {c}^{3}+{b}^{2}{c}^{2}) \left ( d{{\rm e}^{{\frac {x}{2} \left ( b+\sqrt { \left ( -4\,a-4 \right ) c+{b}^{2}} \right ) }}}\sqrt { \left ( -4\,a-4 \right ) c+{b}^{2}}+ \left ( {{\rm e}^{x\sqrt { \left ( -4\,a-4 \right ) c+{b}^{2}}}}{\it \_C1}-{\it \_C2} \right ) c \left ( a+1 \right ) \right ) ^{-2}} \right ) ^{- \left ( 2\,a+2 \right ) ^{-1}} \right \} \]