2.364   ODE No. 364

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

$$\text{Global}\stackrel{`}{}\text{x}{\text{Global}\stackrel{`}{}\text{y}}^{\prime }(\text{Global}\stackrel{`}{}\text{x})(\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})\sin \left(\frac{\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})}{\text{Global}\stackrel{`}{}\text{x}}\right)-\text{Global}\stackrel{`}{}\text{x}\cos \left(\frac{\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})}{\text{Global}\stackrel{`}{}\text{x}}\right))-\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})(\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})\sin \left(\frac{\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})}{\text{Global}\stackrel{`}{}\text{x}}\right)+\text{Global}\stackrel{`}{}\text{x}\cos \left(\frac{\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})}{\text{Global}\stackrel{`}{}\text{x}}\right))=0$$ ✓ Mathematica : cpu = 0.063367 (sec), leaf count = 31

$$\text{Solve}[-\log \left(\frac{\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})}{\text{Global}\stackrel{`}{}\text{x}}\right)-\log (\cos \left(\frac{\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})}{\text{Global}\stackrel{`}{}\text{x}}\right))=c_1+2\log (\text{Global}\stackrel{`}{}\text{x}),\text{Global}\stackrel{`}{}\text{y}(\text{Global}\stackrel{`}{}\text{x})]$$

✓ Maple : cpu = 0.095 (sec), leaf count = 23

$$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}}{\cos \left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\mathit{\_}\mathit{Z}{x}^2\cos \left(\mathit{\_}\mathit{Z}\right)+\mathit{\_}\mathit{C}\mathit{1})\right)x}\}$$