2.642   ODE No. 642

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

$$y^{\prime }(x)=\frac{{(4ax-y(x{)}^2)}^2}{y(x)}$$ ✓ Mathematica : cpu = 0.162656 (sec), leaf count = 105

$$\{\{y(x)\to -\sqrt{4ax-\sqrt{2}\sqrt{a}\tanh \left(\frac{2\sqrt{2}ax-\sqrt{2}{c}_1}{\sqrt{a}}\right)}\},\{y(x)\to \sqrt{4ax-\sqrt{2}\sqrt{a}\tanh \left(\frac{2\sqrt{2}ax-\sqrt{2}{c}_1}{\sqrt{a}}\right)}\}\}$$ ✓ Maple : cpu = 0.414 (sec), leaf count = 286

$$\{y\left(x\right)=\sqrt{4}\sqrt{(\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{2x(\sqrt{2}\sqrt{a}-2ax)}+{\mathrm{e}}^{-2x(\sqrt{2}\sqrt{a}+2ax)})(\mathit{\_}\mathit{C}\mathit{1}(ax-\frac{\sqrt{2}}{4}\sqrt{a}){\mathrm{e}}^{2x(\sqrt{2}\sqrt{a}-2ax)}+{\mathrm{e}}^{-2x(\sqrt{2}\sqrt{a}+2ax)}(ax+\frac{\sqrt{2}}{4}\sqrt{a}))}{(\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{2x(\sqrt{2}\sqrt{a}-2ax)}+{\mathrm{e}}^{-2x(\sqrt{2}\sqrt{a}+2ax)})}^{-1},y\left(x\right)=-\sqrt{4}\sqrt{(\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{2x(\sqrt{2}\sqrt{a}-2ax)}+{\mathrm{e}}^{-2x(\sqrt{2}\sqrt{a}+2ax)})(\mathit{\_}\mathit{C}\mathit{1}(ax-\frac{\sqrt{2}}{4}\sqrt{a}){\mathrm{e}}^{2x(\sqrt{2}\sqrt{a}-2ax)}+{\mathrm{e}}^{-2x(\sqrt{2}\sqrt{a}+2ax)}(ax+\frac{\sqrt{2}}{4}\sqrt{a}))}{(\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{2x(\sqrt{2}\sqrt{a}-2ax)}+{\mathrm{e}}^{-2x(\sqrt{2}\sqrt{a}+2ax)})}^{-1}\}$$