\[ 2 y(x) y''(x)-y'(x)^2-8 y(x)^3-4 y(x)^2=0 \] ✓ Mathematica : cpu = 1.30115 (sec), leaf count = 351
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {i \text {$\#$1} \sqrt {4+\frac {2 c_1}{\text {$\#$1}-\text {$\#$1} \sqrt {1-c_1}}} \sqrt {2+\frac {c_1}{\text {$\#$1}+\text {$\#$1} \sqrt {1-c_1}}} F\left (i \sinh ^{-1}\left (\frac {\sqrt {\frac {c_1}{2 \sqrt {1-c_1}+2}}}{\sqrt {\text {$\#$1}}}\right )|\frac {\sqrt {1-c_1}+1}{1-\sqrt {1-c_1}}\right )}{\sqrt {\frac {c_1}{1+\sqrt {1-c_1}}} \sqrt {4 \text {$\#$1}^2+4 \text {$\#$1}+c_1}}\& \right ][x+c_2]\right \},\left \{y(x)\to \text {InverseFunction}\left [\frac {i \text {$\#$1} \sqrt {4+\frac {2 c_1}{\text {$\#$1}-\text {$\#$1} \sqrt {1-c_1}}} \sqrt {2+\frac {c_1}{\text {$\#$1}+\text {$\#$1} \sqrt {1-c_1}}} F\left (i \sinh ^{-1}\left (\frac {\sqrt {\frac {c_1}{2 \sqrt {1-c_1}+2}}}{\sqrt {\text {$\#$1}}}\right )|\frac {\sqrt {1-c_1}+1}{1-\sqrt {1-c_1}}\right )}{\sqrt {\frac {c_1}{1+\sqrt {1-c_1}}} \sqrt {4 \text {$\#$1}^2+4 \text {$\#$1}+c_1}}\& \right ][x+c_2]\right \}\right \}\] ✓ Maple : cpu = 1.265 (sec), leaf count = 61
\[\left \{-c_{2}-x +\int _{}^{y \left (x \right )}\frac {1}{\sqrt {4 \textit {\_a}^{3}+4 \textit {\_a}^{2}+c_{1} \textit {\_a}}}d \textit {\_a} = 0, -c_{2}-x +\int _{}^{y \left (x \right )}-\frac {1}{\sqrt {\left (4 \textit {\_a}^{2}+4 \textit {\_a} +c_{1}\right ) \textit {\_a}}}d \textit {\_a} = 0\right \}\]