\[ y'(x)=\frac {1}{2} i x y(x) \left (-2 \sqrt {4 \log (a)-x^2+4 \log (y(x))}+i\right ) \] ✓ Mathematica : cpu = 0.590861 (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 = 0.365 (sec), leaf count = 70
\[\left \{-\frac {i x^{2}}{2}-c_{1}+\frac {\arctan \left (\sqrt {-x^{2}+4 \ln \left (a \right )+4 \ln \left (y \left (x \right )\right )}\right )}{2}-\frac {i \ln \left (x^{2}-4 \ln \left (a \right )-4 \ln \left (y \left (x \right )\right )-1\right )}{4}-\frac {\sqrt {-x^{2}+4 \ln \left (a \right )+4 \ln \left (y \left (x \right )\right )}}{2} = 0\right \}\]