8.178   ODE No. 1768

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

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

Mathematica: cpu = 0.113014 (sec), leaf count = 87 $$\{\{y(x)\to -x-\sqrt{-e^{2c_2}{x}^2-2i{c}_1{x}^2+e^{2c_2}+x^2}\},\{y(x)\to -x+\sqrt{-e^{2c_2}{x}^2-2i{c}_1{x}^2+e^{2c_2}+x^2}\}\}$$

Maple: cpu = 1.544 (sec), leaf count = 43 $$\{y\left(x\right)=-x-\sqrt{-\mathit{\_}\mathit{C}\mathit{2}{x}^2+x^2+\mathit{\_}\mathit{C}\mathit{1}},y\left(x\right)=-x+\sqrt{-\mathit{\_}\mathit{C}\mathit{2}{x}^2+x^2+\mathit{\_}\mathit{C}\mathit{1}}\}$$