3.875   ODE No. 875

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=-\frac{-xy\left(x\right)-y\left(x\right)+x^5\sqrt{{\left(y\left(x\right)\right)}^2+x^2}-x^4\sqrt{{\left(y\left(x\right)\right)}^2+x^2}y\left(x\right)}{x(1+x)}=0}}$$

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

Mathematica: cpu = 0.293537 (sec), leaf count = 285 $$\left\{\{y(x)\to \frac{x(2(x+1{)}^{\sqrt{2}}\exp (\sqrt{2}{c}_1+\frac{x^4}{2\sqrt{2}}+\frac{x^2}{\sqrt{2}}+\frac{1}{3}\sqrt{2}(x^2+3)x+\frac{25}{6\sqrt{2}})+(x+1{)}^{2\sqrt{2}}(-e^{2\sqrt{2}{c}_1+\frac{x^4}{\sqrt{2}}+\sqrt{2}{x}^2})+e^{\frac{2}{3}\sqrt{2}x(x^2+3)+\frac{25}{3\sqrt{2}}})}{-2(x+1{)}^{\sqrt{2}}\exp (\sqrt{2}{c}_1+\frac{x^4}{2\sqrt{2}}+\frac{x^2}{\sqrt{2}}+\frac{1}{3}\sqrt{2}(x^2+3)x+\frac{25}{6\sqrt{2}})+(x+1{)}^{2\sqrt{2}}(-e^{2\sqrt{2}{c}_1+\frac{x^4}{\sqrt{2}}+\sqrt{2}{x}^2})+e^{\frac{2}{3}\sqrt{2}x(x^2+3)+\frac{25}{3\sqrt{2}}}}\}\right\}$$

Maple: cpu = 0.187 (sec), leaf count = 79 $$\{\ln \left(2\frac{x(\sqrt{2{\left(y\left(x\right)\right)}^2+2x^2}+y\left(x\right)+x)}{y\left(x\right)-x}\right)+\frac{\sqrt{2}{x}^4}{4}-\frac{\sqrt{2}{x}^3}{3}+\frac{\sqrt{2}{x}^2}{2}-x\sqrt{2}-\ln \left(x\right)+\sqrt{2}\ln (1+x)-\mathit{\_}\mathit{C}\mathit{1}=0\}$$