3.629   ODE No. 629

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{{(2y\left(x\right)\ln \left(x\right)-1)}^2}{x}=0}}$$

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

Mathematica: cpu = 0.780599 (sec), leaf count = 47 $$\left\{\{y(x)\to \frac{1}{\sqrt{2}(\sqrt{2}\log (x)-\tan \left(\frac{1}{2}(\sqrt{2}{c}_1+2\sqrt{2}\log (x))\right))}\}\right\}$$

Maple: cpu = 0.172 (sec), leaf count = 72 $$\{y\left(x\right)=\frac{\sin (\sqrt{2}\ln \left(x\right))\mathit{\_}\mathit{C}\mathit{1}+\cos (\sqrt{2}\ln \left(x\right))}{(2\sin (\sqrt{2}\ln \left(x\right))\mathit{\_}\mathit{C}\mathit{1}+2\cos (\sqrt{2}\ln \left(x\right)))\ln \left(x\right)+\sqrt{2}\cos (\sqrt{2}\ln \left(x\right))\mathit{\_}\mathit{C}\mathit{1}-\sqrt{2}\sin (\sqrt{2}\ln \left(x\right))}\}$$