\[ 2 y(x) y''(x)-y'(x)^2-3 y(x)^4=0 \] ✓ Mathematica : cpu = 8.55933 (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 = 1.409 (sec), leaf count = 49
\[\left \{-c_{2}-x +\int _{}^{y \left (x \right )}\frac {1}{\sqrt {\textit {\_a}^{4}+c_{1} \textit {\_a}}}d \textit {\_a} = 0, -c_{2}-x +\int _{}^{y \left (x \right )}-\frac {1}{\sqrt {\textit {\_a}^{4}+c_{1} \textit {\_a}}}d \textit {\_a} = 0\right \}\]