\[ 2 y(x) y''(x)-y'(x)^2 \left (y'(x)^2+1\right )=0 \] ✓ Mathematica : cpu = 0.564417 (sec), leaf count = 155
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-i e^{-c_1} \sqrt {-1+\text {$\#$1} e^{2 c_1}} \left (\sqrt {\text {$\#$1}}+\frac {e^{-c_1} \sin ^{-1}\left (\sqrt {\text {$\#$1}} e^{c_1}\right )}{\sqrt {1-\text {$\#$1} e^{2 c_1}}}\right )\& \right ][x+c_2]\right \},\left \{y(x)\to \text {InverseFunction}\left [i e^{-c_1} \sqrt {-1+\text {$\#$1} e^{2 c_1}} \left (\sqrt {\text {$\#$1}}+\frac {e^{-c_1} \sin ^{-1}\left (\sqrt {\text {$\#$1}} e^{c_1}\right )}{\sqrt {1-\text {$\#$1} e^{2 c_1}}}\right )\& \right ][x+c_2]\right \}\right \}\] ✓ Maple : cpu = 1.232 (sec), leaf count = 823
\[y \relax (x ) = \frac {\tan \left (\RootOf \left (\left (\tan ^{2}\left (\textit {\_Z} \right )\right ) c_{1}^{2} \textit {\_Z}^{2}-4 \left (\tan ^{2}\left (\textit {\_Z} \right )\right ) c_{1} c_{2} \textit {\_Z} -4 \left (\tan ^{2}\left (\textit {\_Z} \right )\right ) c_{1} x \textit {\_Z} +4 \left (\tan ^{2}\left (\textit {\_Z} \right )\right ) c_{2}^{2}+8 \left (\tan ^{2}\left (\textit {\_Z} \right )\right ) x c_{2}+4 \left (\tan ^{2}\left (\textit {\_Z} \right )\right ) x^{2}+c_{1}^{2} \textit {\_Z}^{2}-4 c_{1} \textit {\_Z} c_{2}-4 c_{1} \textit {\_Z} x -c_{1}^{2}+4 c_{2}^{2}+8 x c_{2}+4 x^{2}\right )\right ) \left (-\RootOf \left (\left (\tan ^{2}\left (\textit {\_Z} \right )\right ) c_{1}^{2} \textit {\_Z}^{2}-4 \left (\tan ^{2}\left (\textit {\_Z} \right )\right ) c_{1} c_{2} \textit {\_Z} -4 \left (\tan ^{2}\left (\textit {\_Z} \right )\right ) c_{1} x \textit {\_Z} +4 \left (\tan ^{2}\left (\textit {\_Z} \right )\right ) c_{2}^{2}+8 \left (\tan ^{2}\left (\textit {\_Z} \right )\right ) x c_{2}+4 \left (\tan ^{2}\left (\textit {\_Z} \right )\right ) x^{2}+c_{1}^{2} \textit {\_Z}^{2}-4 c_{1} \textit {\_Z} c_{2}-4 c_{1} \textit {\_Z} x -c_{1}^{2}+4 c_{2}^{2}+8 x c_{2}+4 x^{2}\right ) c_{1}+2 c_{2}+2 x \right )}{2}+\frac {c_{1}}{2}\]