\[ \boxed { 2\, \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) y \left ( x \right ) - \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2} \left ( \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+1 \right ) =0} \]
Mathematica: cpu = 0.974624 (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 = 1.670 (sec), leaf count = 95 \[ \left \{ -{\frac {{\it \_C1}}{2}\arctan \left ( {1 \left ( y \left ( x \right ) -{\frac {{\it \_C1}}{2}} \right ) {\frac {1}{\sqrt {{\it \_C1} \,y \left ( x \right ) - \left ( y \left ( x \right ) \right ) ^{2}}}}} \right ) }-\sqrt {{\it \_C1}\,y \left ( x \right ) - \left ( y \left ( x \right ) \right ) ^{2}}-x-{\it \_C2}=0,{\frac {{\it \_C1}}{2}\arctan \left ( {1 \left ( y \left ( x \right ) -{\frac {{\it \_C1}}{2}} \right ) {\frac {1}{\sqrt {{\it \_C1}\,y \left ( x \right ) - \left ( y \left ( x \right ) \right ) ^{2}}}}} \right ) }+\sqrt {{\it \_C1}\,y \left ( x \right ) - \left ( y \left ( x \right ) \right ) ^{2}}-x-{\it \_C2}=0 \right \} \]