\[ (x-y(x)) y''(x)-\left (y'(x)+1\right ) \left (y'(x)^2+1\right )=0 \] ✓ Mathematica : cpu = 1.7203 (sec), leaf count = 75
\[\left \{\left \{y(x)\to -\sqrt {-x^2-2 c_2 x+e^{2 c_1}-c_2{}^2}-c_2\right \},\left \{y(x)\to \sqrt {-x^2-2 c_2 x+e^{2 c_1}-c_2{}^2}-c_2\right \}\right \}\] ✓ Maple : cpu = 3.479 (sec), leaf count = 105
\[ \left \{ y \left ( x \right ) =x+{\it RootOf} \left ( -x+\int ^{{\it \_Z}}\!{({{\it \_C1}}^{2}{{\it \_f}}^{2}-1) \left ( {\it \_C1}\,\sqrt {-{{\it \_C1}}^{2}{{\it \_f}}^{2}+2}{\it \_f}-{{\it \_C1}}^{2}{{\it \_f}}^{2}+2 \right ) ^{-1}}{d{\it \_f}}+{\it \_C2} \right ) ,y \left ( x \right ) =x+{\it RootOf} \left ( -x+\int ^{{\it \_Z}}\!-{({{\it \_C1}}^{2}{{\it \_f}}^{2}-1) \left ( {{\it \_C1}}^{2}{{\it \_f}}^{2}+{\it \_C1}\,\sqrt {-{{\it \_C1}}^{2}{{\it \_f}}^{2}+2}{\it \_f}-2 \right ) ^{-1}}{d{\it \_f}}+{\it \_C2} \right ) \right \} \]