3.806   ODE No. 806

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

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

Mathematica: cpu = 0.269534 (sec), leaf count = 23 $$\left\{\{y(x)\to {\tan }^{-1}\left(\frac{-c_1+x-\log (x+1)+1}{x}\right)\}\right\}$$

Maple: cpu = 0.468 (sec), leaf count = 22 $$\{y\left(x\right)=-\arctan \left(\frac{\ln (1+x)-x-\mathit{\_}\mathit{C}\mathit{1}}{x}\right)\}$$