2.1938   ODE No. 1938

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

$$\{x^{″}(t)=\frac{x(t)f^{\prime }(r)}{r},y^{″}(t)=\frac{y(t)f^{\prime }(r)}{r},z^{″}(t)=\frac{z(t)f^{\prime }(r)}{r}\}$$ ✓ Mathematica : cpu = 0.0103403 (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 = 0.132 (sec), leaf count = 101

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