3.879   ODE No. 879

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

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

Mathematica: cpu = 0.152519 (sec), leaf count = 135 $$\left\{\{y(x)\to \frac{x(-2(x+1{)}^{\sqrt{2}}{e}^{\sqrt{2}{c}_1+\sqrt{2}x}+e^{2\sqrt{2}{c}_1+2\sqrt{2}x}-(x+1{)}^{2\sqrt{2}})}{2(x+1{)}^{\sqrt{2}}{e}^{\sqrt{2}{c}_1+\sqrt{2}x}+e^{2\sqrt{2}{c}_1+2\sqrt{2}x}-(x+1{)}^{2\sqrt{2}}}\}\right\}$$

Maple: cpu = 0.172 (sec), leaf count = 55 $$\{\ln \left(2\frac{x(\sqrt{2{\left(y\left(x\right)\right)}^2+2x^2}+y\left(x\right)+x)}{y\left(x\right)-x}\right)+x\sqrt{2}-\ln \left(x\right)-\sqrt{2}\ln (1+x)-\mathit{\_}\mathit{C}\mathit{1}=0\}$$