3.525   ODE No. 525

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

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

Mathematica: cpu = 0.063008 (sec), leaf count = 135 $$\{\{y(x)\to c_1\exp \left(\frac{1}{2}(\frac{a{x}^2}{2}+\frac{1}{2}\sqrt{a}x\sqrt{a{x}^2-8}-4\log (\sqrt{a}\sqrt{a{x}^2-8}+ax))\right)\},\{y(x)\to c_1\exp \left(\frac{1}{2}(\frac{a{x}^2}{2}-\frac{1}{2}\sqrt{a}x\sqrt{a{x}^2-8}+4\log (\sqrt{a}\sqrt{a{x}^2-8}+ax))\right)\}\}$$

Maple: cpu = 0.062 (sec), leaf count = 125 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{(a^{2}x\frac{1}{\sqrt{a^2}}+\sqrt{a^2{x}^2-8a})}^{-2\frac{a}{\sqrt{a^2}}}{\mathrm{e}}^{\frac{a{x}^2}{4}+\frac{x}{4}\sqrt{a^2{x}^2-8a}},y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{(a^{2}x\frac{1}{\sqrt{a^2}}+\sqrt{a^2{x}^2-8a})}^{2\frac{a}{\sqrt{a^2}}}{\mathrm{e}}^{\frac{a{x}^2}{4}-\frac{x}{4}\sqrt{a^2{x}^2-8a}}\}$$