\[ a y'(x)^2+b y(x)^3+y(x) y''(x)=0 \] ✓ Mathematica : cpu = 58.0614 (sec), leaf count = 277
\[\left \{\text {Solve}\left [\frac {y(x) \sqrt {(2 a+3) y(x)^{2 a}} \sqrt {1-\frac {2 b y(x)^{2 a+3}}{2 a c_1+3 c_1}} \, _2F_1\left (\frac {1}{2},\frac {a+1}{2 a+3};\frac {a+1}{2 a+3}+1;\frac {2 b y(x)^{2 a+3}}{2 a c_1+3 c_1}\right )}{(a+1) \sqrt {-2 b y(x)^{2 a+3}+2 a c_1+3 c_1}}=-x+c_2,y(x)\right ],\text {Solve}\left [\frac {y(x) \sqrt {(2 a+3) y(x)^{2 a}} \sqrt {1-\frac {2 b y(x)^{2 a+3}}{2 a c_1+3 c_1}} \, _2F_1\left (\frac {1}{2},\frac {a+1}{2 a+3};\frac {a+1}{2 a+3}+1;\frac {2 b y(x)^{2 a+3}}{2 a c_1+3 c_1}\right )}{(a+1) \sqrt {-2 b y(x)^{2 a+3}+2 a c_1+3 c_1}}=x+c_2,y(x)\right ]\right \}\] ✓ Maple : cpu = 1.49 (sec), leaf count = 107
\[\left \{-c_{2}-x +\int _{}^{y \left (x \right )}\frac {\left (2 a +3\right ) \textit {\_a}^{2 a}}{\sqrt {-\left (2 a +3\right ) \left (2 b \,\textit {\_a}^{2 a +3}-c_{1}\right ) \textit {\_a}^{2 a}}}d \textit {\_a} = 0, -c_{2}-x +\int _{}^{y \left (x \right )}\frac {\left (-2 a -3\right ) \textit {\_a}^{2 a}}{\sqrt {-\left (2 a +3\right ) \left (2 b \,\textit {\_a}^{2 a +3}-c_{1}\right ) \textit {\_a}^{2 a}}}d \textit {\_a} = 0\right \}\]