3.968   ODE No. 968

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=1/2\frac{1}{x(1+x)}(-\sin \left(\frac{y\left(x\right)}{x}\right)y\left(x\right)x-y\left(x\right)\sin \left(\frac{y\left(x\right)}{x}\right)+y\left(x\right)\sin \left(3/2\frac{y\left(x\right)}{x}\right)\cos \left(1/2\frac{y\left(x\right)}{x}\right)x+y\left(x\right)\sin \left(3/2\frac{y\left(x\right)}{x}\right)\cos \left(1/2\frac{y\left(x\right)}{x}\right)+y\left(x\right)\cos \left(1/2\frac{y\left(x\right)}{x}\right)\sin \left(1/2\frac{y\left(x\right)}{x}\right)x+y\left(x\right)\cos \left(1/2\frac{y\left(x\right)}{x}\right)\sin \left(1/2\frac{y\left(x\right)}{x}\right)+2\sin \left(\frac{y\left(x\right)}{x}\right)x^4\cos \left(1/2\frac{y\left(x\right)}{x}\right)\sin \left(1/2\frac{y\left(x\right)}{x}\right)){(\cos \left(\frac{y\left(x\right)}{x}\right))}^{-1}{(\cos \left(1/2\frac{y\left(x\right)}{x}\right))}^{-1}{(\sin \left(1/2\frac{y\left(x\right)}{x}\right))}^{-1}=0}}$$

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

Mathematica: cpu = 0.084511 (sec), leaf count = 30 $$\left\{\{y(x)\to x{\sin }^{-1}((x+1)e^{c_1+\frac{x^2}{2}-x-\frac{3}{2}})\}\right\}$$

Maple: cpu = 0.109 (sec), leaf count = 45 $$\{y\left(x\right)=\frac{x}{2}\arccos (\frac{{\mathrm{e}}^{x^2}\mathit{\_}\mathit{C}\mathit{1}{x}^2}{{\left({\mathrm{e}}^x\right)}^2}+2\frac{{\mathrm{e}}^{x^2}\mathit{\_}\mathit{C}\mathit{1}x}{{\left({\mathrm{e}}^x\right)}^2}+\frac{{\mathrm{e}}^{x^2}\mathit{\_}\mathit{C}\mathit{1}}{{\left({\mathrm{e}}^x\right)}^2}+1)\}$$