3.670   ODE No. 670

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=i/2x(i-2\sqrt{-x^2+4\ln \left(a\right)+4\ln \left(y\left(x\right)\right)})y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.370047 (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 = 0.250 (sec), leaf count = 70 $$\{\frac{1}{2}\sqrt{-x^2+4\ln \left(a\right)+4\ln \left(y\left(x\right)\right)}-\frac{1}{2}\arctan \left(\sqrt{-x^2+4\ln \left(a\right)+4\ln \left(y\left(x\right)\right)}\right)+\frac{i}{4}\ln (x^2-4\ln \left(a\right)-4\ln \left(y\left(x\right)\right)-1)+\frac{i}{2}{x}^2-\mathit{\_}\mathit{C}\mathit{1}=0\}$$