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 = 0.352623 (sec), leaf count = 30

$$\left\{\{y(x)\to x{\sin }^{-1}((x+1)e^{\frac{x^2}{2}-x-\frac{3}{2}+c_1})\}\right\}$$ ✓ Maple : cpu = 0.597 (sec), leaf count = 22

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