\[ \boxed { 2\, \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) y \left ( x \right ) + \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+1=0} \]
Mathematica: cpu = 0.172522 (sec), leaf count = 129 \[ \left \{\left \{y(x)\to \text {InverseFunction}\left [e^{2 c_1} \tan ^{-1}\left (\frac {\sqrt {\text {$\#$1}}}{\sqrt {e^{2 c_1}-\text {$\#$1}}}\right )-\sqrt {\text {$\#$1}} \sqrt {e^{2 c_1}-\text {$\#$1}}\& \right ]\left [c_2+x\right ]\right \},\left \{y(x)\to \text {InverseFunction}\left [\sqrt {\text {$\#$1}} \sqrt {e^{2 c_1}-\text {$\#$1}}-e^{2 c_1} \tan ^{-1}\left (\frac {\sqrt {\text {$\#$1}}}{\sqrt {e^{2 c_1}-\text {$\#$1}}}\right )\& \right ]\left [c_2+x\right ]\right \}\right \} \]
Maple: cpu = 1.716 (sec), leaf count = 95 \[ \left \{ -\sqrt {{\it \_C1}\,y \left ( x \right ) - \left ( y \left ( x \right ) \right ) ^{2}}+{\frac {{\it \_C1}}{2}\arctan \left ( {1 \left ( y \left ( x \right ) -{\frac {{\it \_C1}}{2}} \right ) {\frac {1} {\sqrt {{\it \_C1}\,y \left ( x \right ) - \left ( y \left ( x \right ) \right ) ^{2}}}}} \right ) }-x-{\it \_C2}=0,\sqrt {{\it \_C1}\,y \left ( x \right ) - \left ( y \left ( x \right ) \right ) ^{2}}-{\frac {{ \it \_C1}}{2}\arctan \left ( {1 \left ( y \left ( x \right ) -{\frac {{ \it \_C1}}{2}} \right ) {\frac {1}{\sqrt {{\it \_C1}\,y \left ( x \right ) - \left ( y \left ( x \right ) \right ) ^{2}}}}} \right ) }-x-{ \it \_C2}=0 \right \} \]