\[ 2 y(x) y''(x)-y'(x)^2 \left (y'(x)^2+1\right )=0 \] ✓ Mathematica : cpu = 0.962658 (sec), leaf count = 173
\[\left \{\left \{y(x)\to \text {InverseFunction}\left [-i e^{-c_1} \left (\sqrt {\text {$\#$1}} \sqrt {\text {$\#$1} e^{2 c_1}-1}-e^{-c_1} \log \left (\sqrt {\text {$\#$1}} e^{2 c_1}+e^{c_1} \sqrt {\text {$\#$1} e^{2 c_1}-1}\right )\right )\& \right ]\left [c_2+x\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [i e^{-c_1} \left (\sqrt {\text {$\#$1}} \sqrt {\text {$\#$1} e^{2 c_1}-1}-e^{-c_1} \log \left (\sqrt {\text {$\#$1}} e^{2 c_1}+e^{c_1} \sqrt {\text {$\#$1} e^{2 c_1}-1}\right )\right )\& \right ]\left [c_2+x\right ]\right \}\right \}\]
✓ Maple : cpu = 0.225 (sec), leaf count = 87
\[ \left \{ -{\frac {{\it \_C1}}{2}\arctan \left ( {1 \left ( y \left ( x \right ) -{\frac {{\it \_C1}}{2}} \right ) {\frac {1}{\sqrt {y \left ( x \right ) \left ( {\it \_C1}-y \left ( x \right ) \right ) }}}} \right ) }-\sqrt {y \left ( x \right ) \left ( {\it \_C1}-y \left ( x \right ) \right ) }-x-{\it \_C2}=0,{\frac {{\it \_C1}}{2}\arctan \left ( {1 \left ( y \left ( x \right ) -{\frac {{\it \_C1}}{2}} \right ) {\frac {1}{\sqrt {y \left ( x \right ) \left ( {\it \_C1}-y \left ( x \right ) \right ) }}}} \right ) }+\sqrt {y \left ( x \right ) \left ( {\it \_C1}-y \left ( x \right ) \right ) }-x-{\it \_C2}=0 \right \} \]