\[ 2 y(x) y''(x)-y'(x)^2-8 y(x)^3-4 y(x)^2=0 \] ✓ Mathematica : cpu = 0.961679 (sec), leaf count = 351
DSolve[-4*y[x]^2 - 8*y[x]^3 - Derivative[1][y][x]^2 + 2*y[x]*Derivative[2][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-\frac {i \text {$\#$1} \sqrt {4+\frac {2 c_1}{\text {$\#$1}-\text {$\#$1} \sqrt {1-c_1}}} \sqrt {2+\frac {c_1}{\text {$\#$1}+\text {$\#$1} \sqrt {1-c_1}}} F\left (i \sinh ^{-1}\left (\frac {\sqrt {\frac {c_1}{2 \sqrt {1-c_1}+2}}}{\sqrt {\text {$\#$1}}}\right )|\frac {\sqrt {1-c_1}+1}{1-\sqrt {1-c_1}}\right )}{\sqrt {\frac {c_1}{1+\sqrt {1-c_1}}} \sqrt {4 \text {$\#$1}^2+4 \text {$\#$1}+c_1}}\& \right ][x+c_2]\right \},\left \{y(x)\to \text {InverseFunction}\left [\frac {i \text {$\#$1} \sqrt {4+\frac {2 c_1}{\text {$\#$1}-\text {$\#$1} \sqrt {1-c_1}}} \sqrt {2+\frac {c_1}{\text {$\#$1}+\text {$\#$1} \sqrt {1-c_1}}} F\left (i \sinh ^{-1}\left (\frac {\sqrt {\frac {c_1}{2 \sqrt {1-c_1}+2}}}{\sqrt {\text {$\#$1}}}\right )|\frac {\sqrt {1-c_1}+1}{1-\sqrt {1-c_1}}\right )}{\sqrt {\frac {c_1}{1+\sqrt {1-c_1}}} \sqrt {4 \text {$\#$1}^2+4 \text {$\#$1}+c_1}}\& \right ][x+c_2]\right \}\right \}\] ✓ Maple : cpu = 0.944 (sec), leaf count = 61
dsolve(2*diff(diff(y(x),x),x)*y(x)-diff(y(x),x)^2-8*y(x)^3-4*y(x)^2=0,y(x))
\[\int _{}^{y \left (x \right )}\frac {1}{\sqrt {4 \textit {\_a}^{3}+4 \textit {\_a}^{2}+\textit {\_a} c_{1}}}d \textit {\_a} -x -c_{2} = 0\]