3.342   ODE No. 342

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

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

Mathematica: cpu = 0.261033 (sec), leaf count = 163 $$\{\{y(x)\to -\frac{{\cosh }^{-1}\left(\frac{1}{24}(-5\sqrt{{\log }^2\left(\frac{c_1}{x}\right)+24}-\log \left(\frac{c_1}{x}\right))\right)}{x}\},\{y(x)\to \frac{{\cosh }^{-1}\left(\frac{1}{24}(-5\sqrt{{\log }^2\left(\frac{c_1}{x}\right)+24}-\log \left(\frac{c_1}{x}\right))\right)}{x}\},\{y(x)\to -\frac{{\cosh }^{-1}\left(\frac{1}{24}(5\sqrt{{\log }^2\left(\frac{c_1}{x}\right)+24}-\log \left(\frac{c_1}{x}\right))\right)}{x}\},\{y(x)\to \frac{{\cosh }^{-1}\left(\frac{1}{24}(5\sqrt{{\log }^2\left(\frac{c_1}{x}\right)+24}-\log \left(\frac{c_1}{x}\right))\right)}{x}\}\}$$

Maple: cpu = 0.031 (sec), leaf count = 17 $$\{y\left(x\right)=\frac{1}{x}\ln (-\frac{\ln \left(x\right)}{5}+\frac{\mathit{\_}\mathit{C}\mathit{1}}{5})\}$$