\[ a y(x) y'(x)+b y(x)^3+y''(x)=0 \] ✓ Mathematica : cpu = 34.0885 (sec), leaf count = 92
\[\text {Solve}\left [\int _1^{y(x)}\frac {1}{K[2]^2 \text {InverseFunction}\left [\frac {1}{4} \left (\log (b+\text {$\#$1} (a+2 \text {$\#$1}))-\frac {2 a \tan ^{-1}\left (\frac {a+4 \text {$\#$1}}{\sqrt {8 b-a^2}}\right )}{\sqrt {8 b-a^2}}\right )\& \right ][c_1-\log (K[2])]}dK[2]=x-c_2,y(x)\right ]\] ✓ Maple : cpu = 1.438 (sec), leaf count = 97
\[\left \{-c_{2}-x +\int _{}^{y \left (x \right )}\frac {1}{\RootOf \left (-2 \textit {\_a}^{2} a \arctanh \left (\frac {\textit {\_a}^{2} a +4 \textit {\_Z}}{\sqrt {\left (a^{2}-8 b \right ) \textit {\_a}^{4}}}\right )+c_{1} \sqrt {\left (a^{2}-8 b \right ) \textit {\_a}^{4}}-\sqrt {\left (a^{2}-8 b \right ) \textit {\_a}^{4}}\, \ln \left (\textit {\_a}^{4} b +\textit {\_Z} \,\textit {\_a}^{2} a +2 \textit {\_Z}^{2}\right )\right )}d \textit {\_a} = 0\right \}\]