\[ d y(x)^{1-a}+a y'(x)^2+b y(x) y'(x)+c y(x)^2+y(x) y''(x)=0 \] ✓ Mathematica : cpu = 1.25899 (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 = 0.302 (sec), leaf count = 133
\[y \relax (x ) = {\mathrm e}^{-\frac {x \sqrt {\left (-4 a -4\right ) c +b^{2}}}{2 a +2}} {\mathrm e}^{-\frac {b x}{2 a +2}} \left (\frac {\left (-4 a -4\right ) c^{3}+b^{2} c^{2}}{\left (d \,{\mathrm e}^{\frac {\left (b +\sqrt {\left (-4 a -4\right ) c +b^{2}}\right ) x}{2}} \sqrt {\left (-4 a -4\right ) c +b^{2}}+\left ({\mathrm e}^{x \sqrt {\left (-4 a -4\right ) c +b^{2}}} c_{1}-c_{2}\right ) c \left (a +1\right )\right )^{2}}\right )^{-\frac {1}{2 a +2}}\]