3.671   ODE No. 671

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

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

Mathematica: cpu = 0.426054 (sec), leaf count = 192 $$\{\{y(x)\to -\frac{\sqrt{\sqrt{2}{e}^{\frac{2\sqrt{2}(c_{1}x+1)}{x}}-\frac{2e^{\frac{2\sqrt{2}(c_{1}x+1)}{x}}}{x}-\frac{2}{x}-\sqrt{2}}}{\sqrt{2e^{\frac{2\sqrt{2}(c_{1}x+1)}{x}}+2}}\},\{y(x)\to \frac{\sqrt{\sqrt{2}{e}^{\frac{2\sqrt{2}(c_{1}x+1)}{x}}-\frac{2e^{\frac{2\sqrt{2}(c_{1}x+1)}{x}}}{x}-\frac{2}{x}-\sqrt{2}}}{\sqrt{2e^{\frac{2\sqrt{2}(c_{1}x+1)}{x}}+2}}\}\}$$

Maple: cpu = 0.156 (sec), leaf count = 237 $$\{y\left(x\right)=-\frac{\sqrt{2}}{2x}\sqrt{-(\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{\frac{-1-\sqrt{2}x}{x^2}}+{\mathrm{e}}^{\frac{-1+\sqrt{2}x}{x^2}})(\mathit{\_}\mathit{C}\mathit{1}(\sqrt{2}x+2){\mathrm{e}}^{\frac{-1-\sqrt{2}x}{x^2}}+(2-\sqrt{2}x){\mathrm{e}}^{\frac{-1+\sqrt{2}x}{x^2}})x}{(\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{\frac{-1-\sqrt{2}x}{x^2}}+{\mathrm{e}}^{\frac{-1+\sqrt{2}x}{x^2}})}^{-1},y\left(x\right)=\frac{\sqrt{2}}{2x}\sqrt{-(\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{\frac{-1-\sqrt{2}x}{x^2}}+{\mathrm{e}}^{\frac{-1+\sqrt{2}x}{x^2}})(\mathit{\_}\mathit{C}\mathit{1}(\sqrt{2}x+2){\mathrm{e}}^{\frac{-1-\sqrt{2}x}{x^2}}+(2-\sqrt{2}x){\mathrm{e}}^{\frac{-1+\sqrt{2}x}{x^2}})x}{(\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{\frac{-1-\sqrt{2}x}{x^2}}+{\mathrm{e}}^{\frac{-1+\sqrt{2}x}{x^2}})}^{-1}\}$$