\[ a-x^2-2 x y(x) y'(x)+y(x)^2 y'(x)^2+2 y(x)^2=0 \] ✓ Mathematica : cpu = 0.579728 (sec), leaf count = 63
\[\left \{\left \{y(x)\to -\sqrt {-\frac {a}{2}+4 c_1 x-2 c_1^2-x^2}\right \},\left \{y(x)\to \sqrt {-\frac {a}{2}+4 c_1 x-2 c_1^2-x^2}\right \}\right \}\]
✓ Maple : cpu = 0.434 (sec), leaf count = 145
\[ \left \{ y \left ( x \right ) =\sqrt {-2\,\sqrt {a+2\,{\it \_C1}}x-{\it \_C1}-{x}^{2}-a},y \left ( x \right ) =\sqrt {2\,\sqrt {a+2\,{\it \_C1}}x-{\it \_C1}-{x}^{2}-a},y \left ( x \right ) =-\sqrt {-2\,\sqrt {a+2\,{\it \_C1}}x-{\it \_C1}-{x}^{2}-a},y \left ( x \right ) =-\sqrt {2\,\sqrt {a+2\,{\it \_C1}}x-{\it \_C1}-{x}^{2}-a},y \left ( x \right ) =-{\frac {1}{2}\sqrt {4\,{x}^{2}-2\,a}},y \left ( x \right ) ={\frac {1}{2}\sqrt {4\,{x}^{2}-2\,a}} \right \} \]