3.630   ODE No. 630

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

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

Mathematica: cpu = 0.566572 (sec), leaf count = 101 $$\text{Solve}[\frac{1}{2}b(\log (-b{e}^{-2bx}y(x{)}^2-b{e}^{-bx}y(x)+1)+2bx)=\frac{b{\tan }^{-1}\left(\frac{(b+2)(-e^{bx})-by(x)}{b\sqrt{-\frac{b+4}{b}}(e^{bx}+y(x))}\right)}{\sqrt{-\frac{b+4}{b}}}+c_1,y(x)]$$

Maple: cpu = 0.249 (sec), leaf count = 98 $$\{y\left(x\right)=\frac{1}{{\mathrm{e}}^{-bx}}\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({(\tanh \left(\frac{2\mathit{\_}\mathit{C}\mathit{1}b-2bx-\mathit{\_}\mathit{Z}}{2b}\sqrt{b^2+4b}\right))}^{2}b+4{(\tanh \left(1/2\frac{\sqrt{b^2+4b}(2\mathit{\_}\mathit{C}\mathit{1}b-2bx-\mathit{\_}\mathit{Z})}{b}\right))}^2-4{\mathrm{e}}^{\mathit{\_}\mathit{Z}}-b-4)}-1+\mathit{\_}\mathit{Z}b+b{\mathit{\_}\mathit{Z}}^2)\}$$