2.393   ODE No. 393

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

$$y^{\prime }(x{)}^2+2y(x)\cot (x)y^{\prime }(x)-y(x{)}^2=0$$ ✓ Mathematica : cpu = 0.0314301 (sec), leaf count = 31

$$\{\{y(x)\to c_1{\csc }^2\left(\frac{x}{2}\right)\},\{y(x)\to c_1{\sec }^2\left(\frac{x}{2}\right)\}\}$$

✓ Maple : cpu = 0.119 (sec), leaf count = 85

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