\[ \boxed { \left ( y \left ( x \right ) -x \right ) ^{2} \left ( \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}+1 \right ) -{a}^{2} \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +1 \right ) ^{2}=0} \]
Mathematica: cpu = 95.092075 (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 = 0.718 (sec), leaf count = 130 \[ \left \{ y \left ( x \right ) =x-\sqrt {2}a,y \left ( x \right ) =x+\sqrt {2}a,y \left ( x \right ) =x+{\it RootOf} \left ( -x+\int ^{{\it \_Z}}\!- {\frac {1}{2\,{{\it \_a}}^{2}-4\,{a}^{2}} \left ( {{\it \_a}}^{2}-2\,{a }^{2}+\sqrt {-{{\it \_a}}^{2} \left ( {{\it \_a}}^{2}-2\,{a}^{2} \right ) } \right ) }{d{\it \_a}}+{\it \_C1} \right ) ,y \left ( x \right ) =x+{\it RootOf} \left ( -x+\int ^{{\it \_Z}}\!{\frac {1}{2\,{{ \it \_a}}^{2}-4\,{a}^{2}} \left ( 2\,{a}^{2}-{{\it \_a}}^{2}+\sqrt {-{{ \it \_a}}^{2} \left ( {{\it \_a}}^{2}-2\,{a}^{2} \right ) } \right ) }{d{ \it \_a}}+{\it \_C1} \right ) \right \} \]