2.670   ODE No. 670

1. Problem in Latex
2. Mathematica input
3. Maple input

$$y^{\prime }(x)=\frac{1}{2}ixy(x)(-2\sqrt{4\log (a)-x^2+4\log (y(x))}+i)$$ ✓ Mathematica : cpu = 0.337113 (sec), leaf count = 99

$$\text{Solve}[-\log (y(x))+\frac{1}{4}(-\frac{1}{2}\log (4\log (a)-x^2+4\log (y(x))+1)+i\sqrt{4\log (a)-x^2+4\log (y(x))}-i{\tan }^{-1}\left(\sqrt{4\log (a)-x^2+4\log (y(x))}\right)+4\log (a)-x^2+4\log (y(x)))=c_1,y(x)]$$

✓ Maple : cpu = 0.351 (sec), leaf count = 70

$$\{-\frac{1}{2}\sqrt{-x^2+4\ln \left(a\right)+4\ln \left(y\left(x\right)\right)}+\frac{1}{2}\arctan \left(\sqrt{-x^2+4\ln \left(a\right)+4\ln \left(y\left(x\right)\right)}\right)-\frac{i}{4}\ln (x^2-4\ln \left(a\right)-4\ln \left(y\left(x\right)\right)-1)-\frac{i}{2}{x}^2-\mathit{\_}\mathit{C}\mathit{1}=0\}$$