\[ y'(x)=\frac {1}{2} i x y(x) \left (-2 \sqrt {4 \log (a)-x^2+4 \log (y(x))}+i\right ) \] ✓ Mathematica : cpu = 0.484256 (sec), leaf count = 62
\[\left \{\left \{y(x)\to \exp \left (\frac {1}{4} \left (-4 \log (a)-W\left (i e^{-x^2-1-4 c_1}\right ){}^2-2 W\left (i e^{-x^2-1-4 c_1}\right )+x^2-1\right )\right )\right \}\right \}\] ✓ Maple : cpu = 0.467 (sec), leaf count = 70
\[ \left \{ -{\frac {1}{2}\sqrt {-{x}^{2}+4\,\ln \left ( a \right ) +4\,\ln \left ( y \left ( x \right ) \right ) }}+{\frac {1}{2}\arctan \left ( \sqrt {-{x}^{2}+4\,\ln \left ( a \right ) +4\,\ln \left ( y \left ( x \right ) \right ) } \right ) }-{\frac {i}{4}}\ln \left ( {x}^{2}-4\,\ln \left ( a \right ) -4\,\ln \left ( y \left ( x \right ) \right ) -1 \right ) -{\frac {i}{2}}{x}^{2}-{\it \_C1}=0 \right \} \]