2.827   ODE No. 827

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

$$y^{\prime }(x)=\frac{x^3(-\sqrt{x^2+y(x{)}^2})+x^{2}y(x)\sqrt{x^2+y(x{)}^2}+y(x)}{x}$$ ✓ Mathematica : cpu = 0.255256 (sec), leaf count = 221

$$\{\{y(x)\to \frac{x-2\sqrt{x^2{\tanh }^2\left(\frac{1}{3}(-\sqrt{2}{x}^3-3\sqrt{2}{c}_1)\right)-x^2{\tanh }^4\left(\frac{1}{3}(-\sqrt{2}{x}^3-3\sqrt{2}{c}_1)\right)}}{-1+2{\tanh }^2\left(\frac{1}{3}(-\sqrt{2}{x}^3-3\sqrt{2}{c}_1)\right)}\},\{y(x)\to \frac{x+2\sqrt{x^2{\tanh }^2\left(\frac{1}{3}(-\sqrt{2}{x}^3-3\sqrt{2}{c}_1)\right)-x^2{\tanh }^4\left(\frac{1}{3}(-\sqrt{2}{x}^3-3\sqrt{2}{c}_1)\right)}}{-1+2{\tanh }^2\left(\frac{1}{3}(-\sqrt{2}{x}^3-3\sqrt{2}{c}_1)\right)}\}\}$$ ✓ Maple : cpu = 0.446 (sec), leaf count = 49

$$\{\ln \left(2\frac{x(\sqrt{2{\left(y\left(x\right)\right)}^2+2x^2}+y\left(x\right)+x)}{y\left(x\right)-x}\right)+\frac{\sqrt{2}{x}^3}{3}-\ln \left(x\right)-\mathit{\_}\mathit{C}\mathit{1}=0\}$$