\[ a y(x) y'(x)+b y(x)^3+y''(x)=0 \] ✓ Mathematica : cpu = 32.3944 (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 = 1.038 (sec), leaf count = 97
\[\int _{}^{y \relax (x )}\frac {1}{\RootOf \left (-2 a \,\textit {\_a}^{2} \arctanh \left (\frac {\textit {\_a}^{2} a +4 \textit {\_Z}}{\sqrt {\textit {\_a}^{4} \left (a^{2}-8 b \right )}}\right )-\ln \left (\textit {\_a}^{4} b +\textit {\_Z} \,\textit {\_a}^{2} a +2 \textit {\_Z}^{2}\right ) \sqrt {\textit {\_a}^{4} \left (a^{2}-8 b \right )}+c_{1} \sqrt {\textit {\_a}^{4} \left (a^{2}-8 b \right )}\right )}d \textit {\_a} -x -c_{2} = 0\]