\[ (y(x)-x)^2 \left (y'(x)^2+1\right )-a^2 \left (y'(x)+1\right )^2=0 \] ✓ Mathematica : cpu = 98.9735 (sec), leaf count = 65
\[\left \{\left \{y(x)\to c_1-\sqrt {a^2+2 c_1 x-c_1^2-x^2}\right \},\left \{y(x)\to \sqrt {a^2+2 c_1 x-c_1^2-x^2}+c_1\right \}\right \}\] ✓ Maple : cpu = 1.805 (sec), leaf count = 130
\[ \left \{ y \left ( x \right ) =x-\sqrt {2}a,y \left ( x \right ) =x+\sqrt {2}a,y \left ( x \right ) =x+{\it RootOf} \left ( -x+\int ^{{\it \_Z}}\!-{\frac {1}{2\,{{\it \_a}}^{2}-4\,{a}^{2}} \left ( {{\it \_a}}^{2}-2\,{a}^{2}+\sqrt {-{{\it \_a}}^{4}+2\,{{\it \_a}}^{2}{a}^{2}} \right ) }{d{\it \_a}}+{\it \_C1} \right ) ,y \left ( x \right ) =x+{\it RootOf} \left ( -x+\int ^{{\it \_Z}}\!{\frac {1}{2\,{{\it \_a}}^{2}-4\,{a}^{2}} \left ( 2\,{a}^{2}-{{\it \_a}}^{2}+\sqrt {-{{\it \_a}}^{4}+2\,{{\it \_a}}^{2}{a}^{2}} \right ) }{d{\it \_a}}+{\it \_C1} \right ) \right \} \]