\[ 2 y(x) y''(x)-y'(x)^2-3 y(x)^4=0 \] ✓ Mathematica : cpu = 6.42151 (sec), leaf count = 129
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {2 \sqrt {\text {$\#$1}} \sqrt {1+\frac {\text {$\#$1}^3}{c_1}} \, _2F_1\left (\frac {1}{6},\frac {1}{2};\frac {7}{6};-\frac {\text {$\#$1}^3}{c_1}\right )}{\sqrt {\text {$\#$1}^3+c_1}}\& \right ][x+c_2]\right \},\left \{y(x)\to \text {InverseFunction}\left [\frac {2 \sqrt {\text {$\#$1}} \sqrt {1+\frac {\text {$\#$1}^3}{c_1}} \, _2F_1\left (\frac {1}{6},\frac {1}{2};\frac {7}{6};-\frac {\text {$\#$1}^3}{c_1}\right )}{\sqrt {\text {$\#$1}^3+c_1}}\& \right ][x+c_2]\right \}\right \}\] ✓ Maple : cpu = 0.941 (sec), leaf count = 49
\[\int _{}^{y \relax (x )}\frac {1}{\sqrt {\textit {\_a}^{4}+\textit {\_a} c_{1}}}d \textit {\_a} -x -c_{2} = 0\]