\[ y(x) \left (a+x^2+y(x)^2\right ) y'(x)+x \left (-a+x^2+y(x)^2\right )=0 \] ✓ Mathematica : cpu = 0.163865 (sec), leaf count = 149
DSolve[x*(-a + x^2 + y[x]^2) + y[x]*(a + x^2 + y[x]^2)*Derivative[1][y][x] == 0,y[x],x]
\[\left \{\left \{y(x)\to -\sqrt {-\sqrt {a^2+4 a x^2+4 c_1}-a-x^2}\right \},\left \{y(x)\to \sqrt {-\sqrt {a^2+4 a x^2+4 c_1}-a-x^2}\right \},\left \{y(x)\to -\sqrt {\sqrt {a^2+4 a x^2+4 c_1}-a-x^2}\right \},\left \{y(x)\to \sqrt {\sqrt {a^2+4 a x^2+4 c_1}-a-x^2}\right \}\right \}\] ✓ Maple : cpu = 0.03 (sec), leaf count = 113
dsolve((y(x)^2+x^2+a)*y(x)*diff(y(x),x)+(y(x)^2+x^2-a)*x = 0,y(x))
\[y \left (x \right ) = \sqrt {-x^{2}-a -2 \sqrt {a \,x^{2}-c_{1}}}\]