\[ \boxed { \left ( y \left ( x \right ) \right ) ^{2} \left ( {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) \right ) ^{2}-2\,xy \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +2\, \left ( y \left ( x \right ) \right ) ^{2}-{x}^{2}+a=0} \]
Mathematica: cpu = 0.601076 (sec), leaf count = 70 \[ \left \{\left \{y(x)\to -\frac {\sqrt {-a+8 c_1 x-4 c_1^2-2 x^2}}{\sqrt {2}}\right \},\left \{y(x)\to \frac {\sqrt {-a+8 c_1 x-4 c_1^2-2 x^2}}{\sqrt {2}}\right \}\right \} \]
Maple: cpu = 0.920 (sec), leaf count = 145 \[ \left \{ y \left ( x \right ) =\sqrt {-2\,\sqrt {a+2\,{\it \_C1}}x-{\it \_C1}-{x}^{2}-a},y \left ( x \right ) =\sqrt {2\,\sqrt {a+2\,{\it \_C1}} x-{\it \_C1}-{x}^{2}-a},y \left ( x \right ) =-\sqrt {-2\,\sqrt {a+2\,{ \it \_C1}}x-{\it \_C1}-{x}^{2}-a},y \left ( x \right ) =-\sqrt {2\, \sqrt {a+2\,{\it \_C1}}x-{\it \_C1}-{x}^{2}-a},y \left ( x \right ) =-{ \frac {1}{2}\sqrt {4\,{x}^{2}-2\,a}},y \left ( x \right ) ={\frac {1}{2} \sqrt {4\,{x}^{2}-2\,a}} \right \} \]