2.456   ODE No. 456

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

$$2(1-x^2)y(x)y^{\prime }(x)+x(x^2-1)y^{\prime }(x{)}^2+xy(x{)}^2-x=0$$ ✓ Mathematica : cpu = 0.122107 (sec), leaf count = 421

$$\{\{y(x)\to \frac{-x-x{\tanh }^2\left(\frac{1}{4}(-\frac{i\sqrt{x-1}\sqrt{x+1}\sqrt{(x-1)(x+1)}{\tan }^{-1}\left(\sqrt{x^2-1}\right)}{1-x}-\frac{i\sqrt{x-1}\sqrt{(x-1)(x+1)}{\tan }^{-1}\left(\sqrt{x^2-1}\right)}{\sqrt{x+1}}+2c_1)\right)}{-1+{\tanh }^2\left(\frac{1}{4}(-\frac{i\sqrt{x-1}\sqrt{x+1}\sqrt{(x-1)(x+1)}{\tan }^{-1}\left(\sqrt{x^2-1}\right)}{1-x}-\frac{i\sqrt{x-1}\sqrt{(x-1)(x+1)}{\tan }^{-1}\left(\sqrt{x^2-1}\right)}{\sqrt{x+1}}+2c_1)\right)}\},\{y(x)\to \frac{-x-x{\tanh }^2\left(\frac{1}{4}(\frac{i\sqrt{x-1}\sqrt{x+1}\sqrt{(x-1)(x+1)}{\tan }^{-1}\left(\sqrt{x^2-1}\right)}{1-x}+\frac{i\sqrt{x-1}\sqrt{(x-1)(x+1)}{\tan }^{-1}\left(\sqrt{x^2-1}\right)}{\sqrt{x+1}}+2c_1)\right)}{-1+{\tanh }^2\left(\frac{1}{4}(\frac{i\sqrt{x-1}\sqrt{x+1}\sqrt{(x-1)(x+1)}{\tan }^{-1}\left(\sqrt{x^2-1}\right)}{1-x}+\frac{i\sqrt{x-1}\sqrt{(x-1)(x+1)}{\tan }^{-1}\left(\sqrt{x^2-1}\right)}{\sqrt{x+1}}+2c_1)\right)}\}\}$$ ✓ Maple : cpu = 0.731 (sec), leaf count = 33

$$\{y\left(x\right)=x,y\left(x\right)=-x,y\left(x\right)=\sqrt{-{\mathit{\_}\mathit{C}\mathit{1}}^2+1}+\sqrt{x^2-1}\mathit{\_}\mathit{C}\mathit{1}\}$$