3.410   ODE No. 410

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

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

Mathematica: cpu = 31.055944 (sec), leaf count = 80 $$\text{Solve}[\{x=-\frac{2(2\text{K}\mathrm{\$}\text{1211948}-y(\text{K}\mathrm{\$}\text{1211948}))}{{\text{K}\mathrm{\$}\text{1211948}}^2},y(x)=c_1{e}^{-4(\frac{1}{2}\log (2-\text{K}\mathrm{\$}\text{1211948})-\frac{\log (\text{K}\mathrm{\$}\text{1211948})}{2})}+4e^{-4(\frac{1}{2}\log (2-\text{K}\mathrm{\$}\text{1211948})-\frac{\log (\text{K}\mathrm{\$}\text{1211948})}{2})}(\frac{2}{\text{K}\mathrm{\$}\text{1211948}}+\log (\text{K}\mathrm{\$}\text{1211948}))\},\{y(x),\text{K}\mathrm{\$}\text{1211948}\}]$$

Maple: cpu = 0.546 (sec), leaf count = 64 $$\{y\left(x\right)=\frac{x{\mathrm{e}}^{2\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-x{\mathrm{e}}^{2\mathit{\_}\mathit{Z}}+4x{\mathrm{e}}^{\mathit{\_}\mathit{Z}}-4{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+\mathit{\_}\mathit{C}\mathit{1}+8\mathit{\_}\mathit{Z}-4x)}}{2}+2{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-x{\mathrm{e}}^{2\mathit{\_}\mathit{Z}}+4x{\mathrm{e}}^{\mathit{\_}\mathit{Z}}-4{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+\mathit{\_}\mathit{C}\mathit{1}+8\mathit{\_}\mathit{Z}-4x)}\}$$