\[ a y'(x)^2+b y(x)^3+y(x) y''(x)=0 \] ✓ Mathematica : cpu = 50.889 (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 = 1.13 (sec), leaf count = 107
\[\int _{}^{y \relax (x )}\frac {\textit {\_a}^{2 a} \left (2 a +3\right )}{\sqrt {-\textit {\_a}^{2 a} \left (2 a +3\right ) \left (2 b \,\textit {\_a}^{2 a +3}-c_{1}\right )}}d \textit {\_a} -x -c_{2} = 0\]