3.969   ODE No. 969

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=1/2\frac{1}{x(1+x)}(y\left(x\right)\sin \left(3/2\frac{y\left(x\right)}{x}\right)\cos \left(1/2\frac{y\left(x\right)}{x}\right)x+y\left(x\right)\sin \left(3/2\frac{y\left(x\right)}{x}\right)\cos \left(1/2\frac{y\left(x\right)}{x}\right)+y\left(x\right)\cos \left(1/2\frac{y\left(x\right)}{x}\right)\sin \left(1/2\frac{y\left(x\right)}{x}\right)x+y\left(x\right)\cos \left(1/2\frac{y\left(x\right)}{x}\right)\sin \left(1/2\frac{y\left(x\right)}{x}\right)-\sin \left(\frac{y\left(x\right)}{x}\right)y\left(x\right)x-y\left(x\right)\sin \left(\frac{y\left(x\right)}{x}\right)+2\sin \left(\frac{y\left(x\right)}{x}\right)\cos \left(1/2\frac{y\left(x\right)}{x}\right)\sin \left(1/2\frac{y\left(x\right)}{x}\right)x){(\cos \left(\frac{y\left(x\right)}{x}\right))}^{-1}{(\cos \left(1/2\frac{y\left(x\right)}{x}\right))}^{-1}{(\sin \left(1/2\frac{y\left(x\right)}{x}\right))}^{-1}=0}}$$

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

Mathematica: cpu = 0.058507 (sec), leaf count = 19 $$\left\{\{y(x)\to x{\sin }^{-1}\left(\frac{e^{c_1}x}{x+1}\right)\}\right\}$$

Maple: cpu = 0.125 (sec), leaf count = 27 $$\{y\left(x\right)=\frac{x}{2}\arccos \left(\frac{\mathit{\_}\mathit{C}\mathit{1}{x}^2+x^2+2x+1}{{(1+x)}^2}\right)\}$$