3.904   ODE No. 904

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

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

Mathematica: cpu = 0.051506 (sec), leaf count = 23 $$\left\{\{y(x)\to 2x{\cot }^{-1}\left(e^{-c_1-\frac{x^2}{2}}\right)\}\right\}$$

Maple: cpu = 0.031 (sec), leaf count = 64 $$\{y\left(x\right)=\arctan (2\frac{{\mathrm{e}}^{1/2x^2}\mathit{\_}\mathit{C}\mathit{1}}{{\left({\mathrm{e}}^{1/2x^2}\right)}^2{\mathit{\_}\mathit{C}\mathit{1}}^2+1},-1({\left({\mathrm{e}}^{\frac{x^2}{2}}\right)}^2{\mathit{\_}\mathit{C}\mathit{1}}^2-1){({\left({\mathrm{e}}^{\frac{x^2}{2}}\right)}^2{\mathit{\_}\mathit{C}\mathit{1}}^2+1)}^{-1})x\}$$