\[ -y'(x)^2+2 y(x) y''(x)-8 y(x)^3=0 \] ✓ Mathematica : cpu = 0.740425 (sec), leaf count = 135
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {2 \sqrt {\text {$\#$1}} \sqrt {1+\frac {4 \text {$\#$1}^2}{c_1}} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {5}{4};-\frac {4 \text {$\#$1}^2}{c_1}\right )}{\sqrt {4 \text {$\#$1}^2+c_1}}\& \right ][x+c_2]\right \},\left \{y(x)\to \text {InverseFunction}\left [\frac {2 \sqrt {\text {$\#$1}} \sqrt {1+\frac {4 \text {$\#$1}^2}{c_1}} \, _2F_1\left (\frac {1}{4},\frac {1}{2};\frac {5}{4};-\frac {4 \text {$\#$1}^2}{c_1}\right )}{\sqrt {4 \text {$\#$1}^2+c_1}}\& \right ][x+c_2]\right \}\right \}\] ✓ Maple : cpu = 0.257 (sec), leaf count = 53
\[ \left \{ \int ^{y \left ( x \right ) }\!{\frac {1}{\sqrt {4\,{{\it \_a}}^{3}+{\it \_a}\,{\it \_C1}}}}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!-{\frac {1}{\sqrt {4\,{{\it \_a}}^{3}+{\it \_a}\,{\it \_C1}}}}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \]