8.174   ODE No. 1764

$$\boxed{{\displaystyle xy\left(x\right)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)-2x{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2+(1+y\left(x\right))\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.064508 (sec), leaf count = 52 $$\left\{\{y(x)\to \frac{\tan \left(\frac{1}{2}(\sqrt{2}\sqrt{c_1}\log (x)-\sqrt{2}\sqrt{c_1}{c}_2)\right)}{\sqrt{2}\sqrt{c_1}}\}\right\}$$

Maple: cpu = 1.638 (sec), leaf count = 18 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\tanh \left(\frac{\ln \left(x\right)-\mathit{\_}\mathit{C}\mathit{2}}{2\mathit{\_}\mathit{C}\mathit{1}}\right)\}$$