\[ \boxed { \left ( {\frac {{\rm d}^{2}}{{\rm d}{x}^{2}}}y \left ( x \right ) \right ) \left ( x-y \left ( x \right ) \right ) - \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +1 \right ) \left ( \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+1 \right ) =0} \]
Mathematica: cpu = 0.327042 (sec), leaf count = 75 \[ \left \{\left \{y(x)\to -\sqrt {-2 c_2 x+e^{2 c_1}-c_2^2-x^2}-c_2\right \},\left \{y(x)\to \sqrt {-2 c_2 x+e^{2 c_1}-c_2^2-x^2}-c_2\right \}\right \} \]
Maple: cpu = 1.997 (sec), leaf count = 105 \[ \left \{ y \left ( x \right ) =x+{\it RootOf} \left ( -x+\int ^{{\it \_Z} }\!{({{\it \_C1}}^{2}{{\it \_f}}^{2}-1) \left ( -{{\it \_C1}}^{2}{{\it \_f}}^{2}+{\it \_C1}\,\sqrt {-{{\it \_C1}}^{2}{{\it \_f}}^{2}+2}{\it \_f}+2 \right ) ^{-1}}{d{\it \_f}}+{\it \_C2} \right ) ,y \left ( x \right ) =x+{\it RootOf} \left ( -x+\int ^{{\it \_Z}}\!-{({{\it \_C1}}^ {2}{{\it \_f}}^{2}-1) \left ( {{\it \_C1}}^{2}{{\it \_f}}^{2}+{\it \_C1 }\,\sqrt {-{{\it \_C1}}^{2}{{\it \_f}}^{2}+2}{\it \_f}-2 \right ) ^{-1} }{d{\it \_f}}+{\it \_C2} \right ) \right \} \]