3.456   ODE No. 456

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

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

Mathematica: cpu = 0.122516 (sec), leaf count = 79 $$\{\{y(x)\to x+2x{\sinh }^2\left(\frac{1}{2}(c_1-2i{\tan }^{-1}\left(\frac{\sqrt{x-1}}{\sqrt{x+1}}\right))\right)\},\{y(x)\to x+2x{\sinh }^2\left(\frac{1}{2}(c_1+2i{\tan }^{-1}\left(\frac{\sqrt{x-1}}{\sqrt{x+1}}\right))\right)\}\}$$

Maple: cpu = 0.874 (sec), leaf count = 33 $$\{y\left(x\right)=x,y\left(x\right)=-x,y\left(x\right)=\sqrt{-{\mathit{\_}\mathit{C}\mathit{1}}^2+1}+\sqrt{x^2-1}\mathit{\_}\mathit{C}\mathit{1}\}$$