2.827   ODE No. 827

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

$$y^{\prime }(x)=\frac{x^{2}y(x)\sqrt{x^2+y(x{)}^2}+x^3(-\sqrt{x^2+y(x{)}^2})+y(x)}{x}$$ ✓ Mathematica : cpu = 0.125597 (sec), leaf count = 111

$$\left\{\{y(x)\to \frac{x(-2e^{\sqrt{2}{c}_1+\frac{\sqrt{2}{x}^3}{3}}+e^{2\sqrt{2}{c}_1+\frac{2\sqrt{2}{x}^3}{3}}-1)}{2e^{\sqrt{2}{c}_1+\frac{\sqrt{2}{x}^3}{3}}+e^{2\sqrt{2}{c}_1+\frac{2\sqrt{2}{x}^3}{3}}-1}\}\right\}$$

✓ Maple : cpu = 0.221 (sec), leaf count = 49

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