3.418   ODE No. 418

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

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

Mathematica: cpu = 0.446057 (sec), leaf count = 165 $$\{\text{Solve}[-\frac{\sqrt{\frac{y(x)}{x}}\sqrt{\frac{y(x)}{x}-4a}-4a\log (\sqrt{\frac{y(x)}{x}-4a}+\sqrt{\frac{y(x)}{x}})+\frac{y(x)}{x}}{4a}=c_1+\frac{\log (x)}{2},y(x)],\text{Solve}[\frac{y(x)}{4ax}-\frac{\sqrt{\frac{y(x)}{x}}\sqrt{\frac{y(x)}{x}-4a}}{4a}+\log (\sqrt{\frac{y(x)}{x}-4a}+\sqrt{\frac{y(x)}{x}})=c_1-\frac{\log (x)}{2},y(x)]\}$$

Maple: cpu = 0.515 (sec), leaf count = 55 $$\{y\left(x\right)=0,y\left(x\right)=-a^{2}x{(-\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}(-\frac{x\mathrm{e}}{\mathit{\_}\mathit{C}\mathit{1}a})+1)}^2{(-(-\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}(-\frac{x\mathrm{e}}{\mathit{\_}\mathit{C}\mathit{1}a})+1)a+a)}^{-1}\}$$