3.965   ODE No. 965

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

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

Mathematica: cpu = 0.056007 (sec), leaf count = 29 $$\left\{\{y(x)\to x{\sin }^{-1}\left(x{e}^{c_1+\frac{x^3}{3}+\frac{x^2}{2}}\right)\}\right\}$$

Maple: cpu = 0.093 (sec), leaf count = 25 $$\{y\left(x\right)=\frac{x}{2}\arccos ({\mathrm{e}}^{\frac{2x^3}{3}}{\mathrm{e}}^{x^2}\mathit{\_}\mathit{C}\mathit{1}{x}^2+1)\}$$