2.968   ODE No. 968

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

$$y^{\prime }(x)=\frac{\csc \left(\frac{y(x)}{2x}\right)\sec \left(\frac{y(x)}{2x}\right)\sec \left(\frac{y(x)}{x}\right)(x^4\sin \left(\frac{y(x)}{2x}\right)\sin \left(\frac{y(x)}{x}\right)\cos \left(\frac{y(x)}{2x}\right)-\frac{1}{2}xy(x)\sin \left(\frac{y(x)}{x}\right)-\frac{1}{2}y(x)\sin \left(\frac{y(x)}{x}\right)+\frac{1}{2}xy(x)\sin \left(\frac{y(x)}{2x}\right)\cos \left(\frac{y(x)}{2x}\right)+\frac{1}{2}xy(x)\sin \left(\frac{3y(x)}{2x}\right)\cos \left(\frac{y(x)}{2x}\right)+\frac{1}{2}y(x)\sin \left(\frac{y(x)}{2x}\right)\cos \left(\frac{y(x)}{2x}\right)+\frac{1}{2}y(x)\sin \left(\frac{3y(x)}{2x}\right)\cos \left(\frac{y(x)}{2x}\right))}{x(x+1)}$$ ✓ Mathematica : cpu = 0.0833949 (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 = 0.148 (sec), leaf count = 45

$$\{y\left(x\right)=\frac{x}{2}\arccos (\frac{{\mathrm{e}}^{x^2}\mathit{\_}\mathit{C}\mathit{1}{x}^2}{{\left({\mathrm{e}}^x\right)}^2}+2\frac{{\mathrm{e}}^{x^2}\mathit{\_}\mathit{C}\mathit{1}x}{{\left({\mathrm{e}}^x\right)}^2}+\frac{{\mathrm{e}}^{x^2}\mathit{\_}\mathit{C}\mathit{1}}{{\left({\mathrm{e}}^x\right)}^2}+1)\}$$