8.79   ODE No. 1669

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

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

Mathematica: cpu = 103.487141 (sec), leaf count = 126 $$\text{Solve}[{\int }_1^{y(x)}-\frac{x}{c_1{e}^{xK[1]}+2xK[1]+1}dK[1]-{\int }_1^x(-\frac{y(x)}{c_1{e}^{y(x)K[2]}+2y(x)K[2]+1}-\frac{c_1{e}^{y(x)K[2]}+y(x)K[2]+1}{K[2](c_1{e}^{y(x)K[2]}+2y(x)K[2]+1)}+\frac{1}{c_1{e}^{K[2]}+2K[2]+1})dK[2]=c_2,y(x)]$$

Maple: cpu = 0.094 (sec), leaf count = 32 $$\{y\left(x\right)=\frac{1}{x}\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\ln \left(x\right)+\mathit{\_}\mathit{C}\mathit{2}+{\int }^{\mathit{\_}\mathit{Z}}-{({\mathrm{e}}^{\mathit{\_}\mathit{f}}\mathit{\_}\mathit{C}\mathit{1}-2\mathit{\_}\mathit{f}-1)}^{-1}d\mathit{\_}\mathit{f})\}$$