\[ a-x^2-2 x y(x) y'(x)+y(x)^2 y'(x)^2+2 y(x)^2=0 \] ✓ Mathematica : cpu = 0.420323 (sec), leaf count = 70
DSolve[a - x^2 + 2*y[x]^2 - 2*x*y[x]*Derivative[1][y][x] + y[x]^2*Derivative[1][y][x]^2 == 0,y[x],x]
\[\left \{\left \{y(x)\to -\frac {\sqrt {-a-2 x^2+8 c_1 x-4 c_1{}^2}}{\sqrt {2}}\right \},\left \{y(x)\to \frac {\sqrt {-a-2 x^2+8 c_1 x-4 c_1{}^2}}{\sqrt {2}}\right \}\right \}\] ✓ Maple : cpu = 0.526 (sec), leaf count = 145
dsolve(y(x)^2*diff(y(x),x)^2-2*x*y(x)*diff(y(x),x)+2*y(x)^2-x^2+a = 0,y(x))
\[y \left (x \right ) = -\frac {\sqrt {4 x^{2}-2 a}}{2}\]