\[ -y'(x)^2+2 y(x) y''(x)-8 y(x)^3-4 y(x)^2=0 \] ✓ Mathematica : cpu = 0.968186 (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 = 0.182 (sec), leaf count = 61
\[ \left \{ \int ^{y \left ( x \right ) }\!{\frac {1}{\sqrt {4\,{{\it \_a}}^{3}+{\it \_a}\,{\it \_C1}+4\,{{\it \_a}}^{2}}}}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!-{\frac {1}{\sqrt { \left ( 4\,{{\it \_a}}^{2}+{\it \_C1}+4\,{\it \_a} \right ) {\it \_a}}}}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \]