\[ a-x^2-2 x y(x) y'(x)+y(x)^2 y'(x)^2+2 y(x)^2=0 \] ✓ Mathematica : cpu = 0.420323 (sec), leaf count = 70
\[\left \{\left \{y(x)\to -\frac {\sqrt {-a-2 x^2+8 c_1 x-4 c_1{}^2}}{\sqrt {2}}\right \},\left \{y(x)\to \frac {\sqrt {-a-2 x^2+8 c_1 x-4 c_1{}^2}}{\sqrt {2}}\right \}\right \}\] ✓ Maple : cpu = 0.526 (sec), leaf count = 145
\[y \relax (x ) = -\frac {\sqrt {4 x^{2}-2 a}}{2}\]