11.26   ODE No. 1938

$$\boxed{{\displaystyle \begin{array}{rl}{x}^{″}(t)& =\frac{\partial F}{\partial x}\\ y^{″}(t)& =\frac{\partial F}{\partial y}\\ z^{″}(t)& =\frac{\partial F}{\partial z}\end{array}}}$$

Where $F=F(r)$ and $r=\sqrt{x(t{)}^2+y(t{)}^2+z(t{)}^2}$

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

Mathematica: cpu = 0.011001 (sec), leaf count = 137 $$\left\{\{x(t)\to c_1{e}^{-\frac{t\sqrt{f^{\prime }(r)}}{\sqrt{r}}}+c_2{e}^{\frac{t\sqrt{f^{\prime }(r)}}{\sqrt{r}}},y(t)\to c_3{e}^{-\frac{t\sqrt{f^{\prime }(r)}}{\sqrt{r}}}+c_4{e}^{\frac{t\sqrt{f^{\prime }(r)}}{\sqrt{r}}},z(t)\to c_5{e}^{-\frac{t\sqrt{f^{\prime }(r)}}{\sqrt{r}}}+c_6{e}^{\frac{t\sqrt{f^{\prime }(r)}}{\sqrt{r}}}\}\right\}$$

Maple: cpu = 0.078 (sec), leaf count = 101 $$\left\{\{x\left(t\right)=\mathit{\_}\mathit{C}\mathit{5}{\mathrm{e}}^{t\sqrt{\frac{\mathrm{d}}{\mathrm{d}r}F\left(r\right)}\frac{1}{\sqrt{r}}}+\mathit{\_}\mathit{C}\mathit{6}{\mathrm{e}}^{-t\sqrt{\frac{\mathrm{d}}{\mathrm{d}r}F\left(r\right)}\frac{1}{\sqrt{r}}},y\left(t\right)=\mathit{\_}\mathit{C}\mathit{3}{\mathrm{e}}^{t\sqrt{\frac{\mathrm{d}}{\mathrm{d}r}F\left(r\right)}\frac{1}{\sqrt{r}}}+\mathit{\_}\mathit{C}\mathit{4}{\mathrm{e}}^{-t\sqrt{\frac{\mathrm{d}}{\mathrm{d}r}F\left(r\right)}\frac{1}{\sqrt{r}}},z\left(t\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{t\sqrt{\frac{\mathrm{d}}{\mathrm{d}r}F\left(r\right)}\frac{1}{\sqrt{r}}}+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-t\sqrt{\frac{\mathrm{d}}{\mathrm{d}r}F\left(r\right)}\frac{1}{\sqrt{r}}}\}\right\}$$