2.879   ODE No. 879

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

$$y^{\prime }(x)=\frac{x^2(-\sqrt{x^2+y(x{)}^2})+xy(x)\sqrt{x^2+y(x{)}^2}+xy(x)+y(x)}{x(x+1)}$$ ✓ Mathematica : cpu = 0.313471 (sec), leaf count = 239

$$\{\{y(x)\to \frac{x-2\sqrt{x^2{\tanh }^2(\sqrt{2}x-\sqrt{2}\log (x+1)+\sqrt{2}{c}_1)-x^2{\tanh }^4(\sqrt{2}x-\sqrt{2}\log (x+1)+\sqrt{2}{c}_1)}}{-1+2{\tanh }^2(\sqrt{2}x-\sqrt{2}\log (x+1)+\sqrt{2}{c}_1)}\},\{y(x)\to \frac{x+2\sqrt{x^2{\tanh }^2(\sqrt{2}x-\sqrt{2}\log (x+1)+\sqrt{2}{c}_1)-x^2{\tanh }^4(\sqrt{2}x-\sqrt{2}\log (x+1)+\sqrt{2}{c}_1)}}{-1+2{\tanh }^2(\sqrt{2}x-\sqrt{2}\log (x+1)+\sqrt{2}{c}_1)}\}\}$$ ✓ Maple : cpu = 0.477 (sec), leaf count = 55

$$\{\ln \left(2\frac{x(\sqrt{2{\left(y\left(x\right)\right)}^2+2x^2}+y\left(x\right)+x)}{y\left(x\right)-x}\right)+\sqrt{2}x-\sqrt{2}\ln (1+x)-\ln \left(x\right)-\mathit{\_}\mathit{C}\mathit{1}=0\}$$