3.686   ODE No. 686

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{x{\left(y\left(x\right)\right)}^3{\mathrm{e}}^{2x^2}}{y\left(x\right){\mathrm{e}}^{x^2}+1}=0}}$$

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

Mathematica: cpu = 9.256675 (sec), leaf count = 68 $$\text{Solve}[\log (y(x))-2y(x{)}^2(\frac{\log (e^{2x^2}y(x{)}^2+2e^{x^2}y(x)+2)}{4y(x{)}^2}-\frac{{\tan }^{-1}(e^{x^2}y(x)+1)}{2y(x{)}^2})=c_1,y(x)]$$

Maple: cpu = 1.482 (sec), leaf count = 85 $$\{y\left(x\right)=\frac{1}{{\mathrm{e}}^{x^2}}(-\tan \left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-2x^2-\ln (\frac{81{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2}{10}+\frac{81}{10})+2\ln (9/2\tan \left(\mathit{\_}\mathit{Z}\right)-9/2)+6\mathit{\_}\mathit{C}\mathit{1}-2\mathit{\_}\mathit{Z})\right)+1){(\tan \left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-2x^2-\ln (\frac{81{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2}{10}+\frac{81}{10})+2\ln (9/2\tan \left(\mathit{\_}\mathit{Z}\right)-9/2)+6\mathit{\_}\mathit{C}\mathit{1}-2\mathit{\_}\mathit{Z})\right))}^{-1}\}$$