\[ y'(x)=\frac {1}{2} i x y(x) \left (-2 \sqrt {4 \log (a)-x^2+4 \log (y(x))}+i\right ) \] ✓ Mathematica : cpu = 0.488872 (sec), leaf count = 83
\[\text {Solve}\left [2 i \sqrt {4 \log (a)-x^2+4 \log (y(x))}-2 i \tan ^{-1}\left (\sqrt {4 \log (a)-x^2+4 \log (y(x))}\right )+8 \log (a)=\log \left (4 \log (a)-x^2+4 \log (y(x))+1\right )+8 c_1+2 x^2,y(x)\right ]\]
✓ Maple : cpu = 0.361 (sec), leaf count = 70
\[ \left \{ {\frac {1}{2}\sqrt {-{x}^{2}+4\,\ln \left ( a \right ) +4\,\ln \left ( y \left ( x \right ) \right ) }}-{\frac {1}{2}\arctan \left ( \sqrt {-{x}^{2}+4\,\ln \left ( a \right ) +4\,\ln \left ( y \left ( x \right ) \right ) } \right ) }+{\frac {i}{4}}\ln \left ( {x}^{2}-4\,\ln \left ( a \right ) -4\,\ln \left ( y \left ( x \right ) \right ) -1 \right ) +{\frac {i}{2}}{x}^{2}-{\it \_C1}=0 \right \} \]