3.952   ODE No. 952

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=-\frac{-y\left(x\right)+\sqrt{{\left(y\left(x\right)\right)}^2+x^2}{x}^2-x\sqrt{{\left(y\left(x\right)\right)}^2+x^2}y\left(x\right)+x^4\sqrt{{\left(y\left(x\right)\right)}^2+x^2}-x^3\sqrt{{\left(y\left(x\right)\right)}^2+x^2}y\left(x\right)+x^5\sqrt{{\left(y\left(x\right)\right)}^2+x^2}-x^4\sqrt{{\left(y\left(x\right)\right)}^2+x^2}y\left(x\right)}{x}=0}}$$

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

Mathematica: cpu = 0.139018 (sec), leaf count = 189 $$\left\{\{y(x)\to \frac{x(-2e^{\sqrt{2}{c}_1+\frac{\sqrt{2}{x}^5}{5}+\frac{x^4}{2\sqrt{2}}+\frac{x^2}{\sqrt{2}}}+e^{2\sqrt{2}{c}_1+\frac{2\sqrt{2}{x}^5}{5}+\frac{x^4}{\sqrt{2}}+\sqrt{2}{x}^2}-1)}{2e^{\sqrt{2}{c}_1+\frac{\sqrt{2}{x}^5}{5}+\frac{x^4}{2\sqrt{2}}+\frac{x^2}{\sqrt{2}}}+e^{2\sqrt{2}{c}_1+\frac{2\sqrt{2}{x}^5}{5}+\frac{x^4}{\sqrt{2}}+\sqrt{2}{x}^2}-1}\}\right\}$$

Maple: cpu = 0.202 (sec), leaf count = 65 $$\{\ln \left(2\frac{x(\sqrt{2{\left(y\left(x\right)\right)}^2+2x^2}+y\left(x\right)+x)}{y\left(x\right)-x}\right)+\frac{\sqrt{2}{x}^5}{5}+\frac{\sqrt{2}{x}^4}{4}+\frac{\sqrt{2}{x}^2}{2}-\ln \left(x\right)-\mathit{\_}\mathit{C}\mathit{1}=0\}$$