\[ a y'(x)^2+b y(x)^2 y'(x)+c y(x)^4+y(x) y''(x)=0 \] ✓ Mathematica : cpu = 88.0957 (sec), leaf count = 105
\[\text {Solve}\left [\int _1^{y(x)}\frac {1}{K[2]^2 \text {InverseFunction}\left [\frac {\log (c+\text {$\#$1} (b+(a+2) \text {$\#$1}))-\frac {2 b \tan ^{-1}\left (\frac {b+2 (a+2) \text {$\#$1}}{\sqrt {4 (a+2) c-b^2}}\right )}{\sqrt {4 (a+2) c-b^2}}}{2 (a+2)}\& \right ][c_1-\log (K[2])]}dK[2]=x-c_2,y(x)\right ]\] ✓ Maple : cpu = 1.628 (sec), leaf count = 173
\[\left \{-c_{2}-x +\int _{}^{y \left (x \right )}\frac {2 a +4}{-\textit {\_a}^{2} b +\sqrt {-\textit {\_a}^{4} b^{2}+\left (4 a +8\right ) \textit {\_a}^{4} c}\, \tan \left (\RootOf \left (2 \textit {\_Z} \,\textit {\_a}^{2} b -2 \sqrt {4 \textit {\_a}^{4} a c -\textit {\_a}^{4} b^{2}+8 c \,\textit {\_a}^{4}}\, a \ln \left (\textit {\_a} \right )+c_{1} \sqrt {4 \textit {\_a}^{4} a c -\textit {\_a}^{4} b^{2}+8 c \,\textit {\_a}^{4}}-\sqrt {4 \textit {\_a}^{4} a c -\textit {\_a}^{4} b^{2}+8 c \,\textit {\_a}^{4}}\, \ln \left (\frac {\left (\tan ^{2}\left (\textit {\_Z} \right )+1\right ) \left (4 a c -b^{2}+8 c \right ) \textit {\_a}^{4}}{4 a +8}\right )\right )\right )}d \textit {\_a} = 0\right \}\]