\[ y'(x)=\frac {1}{2} i x y(x) \left (-2 \sqrt {4 \log (a)-x^2+4 \log (y(x))}+i\right ) \] ✓ Mathematica : cpu = 0.380389 (sec), leaf count = 62
DSolve[Derivative[1][y][x] == (I/2)*x*(I - 2*Sqrt[-x^2 + 4*Log[a] + 4*Log[y[x]]])*y[x],y[x],x]
\[\left \{\left \{y(x)\to \exp \left (\frac {1}{4} \left (-4 \log (a)-W\left (i e^{-x^2-1-4 c_1}\right ){}^2-2 W\left (i e^{-x^2-1-4 c_1}\right )+x^2-1\right )\right )\right \}\right \}\] ✓ Maple : cpu = 0.29 (sec), leaf count = 70
dsolve(diff(y(x),x) = 1/2*I*x*(I-2*(-x^2+4*ln(a)+4*ln(y(x)))^(1/2))*y(x),y(x))
\[-\frac {i \ln \left (x^{2}-4 \ln \left (a \right )-4 \ln \left (y \left (x \right )\right )-1\right )}{4}-\frac {\sqrt {-x^{2}+4 \ln \left (a \right )+4 \ln \left (y \left (x \right )\right )}}{2}+\frac {\arctan \left (\sqrt {-x^{2}+4 \ln \left (a \right )+4 \ln \left (y \left (x \right )\right )}\right )}{2}-\frac {i x^{2}}{2}-c_{1} = 0\]