3.393   ODE No. 393

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

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

Mathematica: cpu = 0.072509 (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 = 0.858 (sec), leaf count = 85 $$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}}{\tan \left(x\right)}\sqrt{1-{({(\tan \left(x\right))}^2+1)}^{-1}}\sqrt{{(\tan \left(x\right))}^2+1}{(1+\frac{1}{\sqrt{{(\tan \left(x\right))}^2+1}})}^{-1},y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}}{\tan \left(x\right)}(1+\frac{1}{\sqrt{{(\tan \left(x\right))}^2+1}})\sqrt{{(\tan \left(x\right))}^2+1}\frac{1}{\sqrt{1-{({(\tan \left(x\right))}^2+1)}^{-1}}}\}$$