\[ \boxed { 2\, \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) y \left ( x \right ) - \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}-8\, \left ( y \left ( x \right ) \right ) ^{3}-4\, \left ( y \left ( x \right ) \right ) ^{2}=0} \]
Mathematica: cpu = 1.403178 (sec), leaf count = 359 \[ \left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {2 i \text {$\#$1} \sqrt {\frac {c_1}{\text {$\#$1} \left (2-2 \sqrt {1-c_1}\right )}+1} \sqrt {\frac {c_1}{\text {$\#$1} \left (2 \sqrt {1-c_1}+2\right )}+1} F\left (i \sinh ^{-1}\left (\frac {\sqrt {\frac {c_1}{2 \sqrt {1-c_1}+2}}}{\sqrt {\text {$\#$1}}}\right )|\frac {\sqrt {1-c_1}+1}{1-\sqrt {1-c_1}}\right )}{\sqrt {\frac {c_1}{2 \sqrt {1-c_1}+2}} \sqrt {4 \text {$\#$1}^2+4 \text {$\#$1}+c_1}}\& \right ]\left [c_2+x\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\frac {2 i \text {$\#$1} \sqrt {\frac {c_1}{\text {$\#$1} \left (2-2 \sqrt {1-c_1}\right )}+1} \sqrt {\frac {c_1}{\text {$\#$1} \left (2 \sqrt {1-c_1}+2\right )}+1} F\left (i \sinh ^{-1}\left (\frac {\sqrt {\frac {c_1}{2 \sqrt {1-c_1}+2}}}{\sqrt {\text {$\#$1}}}\right )|\frac {\sqrt {1-c_1}+1}{1-\sqrt {1-c_1}}\right )}{\sqrt {\frac {c_1}{2 \sqrt {1-c_1}+2}} \sqrt {4 \text {$\#$1}^2+4 \text {$\#$1}+c_1}}\& \right ]\left [c_2+x\right ]\right \}\right \} \]
Maple: cpu = 1.653 (sec), leaf count = 63 \[ \left \{ \int ^{y \left ( x \right ) }\!{\frac {1}{\sqrt {4\,{{\it \_a}} ^{3}+{\it \_a}\,{\it \_C1}+4\,{{\it \_a}}^{2}}}}{d{\it \_a}}-x-{\it \_C2}=0,\int ^{y \left ( x \right ) }\!-{\frac {1}{\sqrt {4\,{{\it \_a}} ^{3}+{\it \_a}\,{\it \_C1}+4\,{{\it \_a}}^{2}}}}{d{\it \_a}}-x-{\it \_C2}=0 \right \} \]