\[ \left \{x''(t)=\frac {x(t) f'(r)}{r},y''(t)=\frac {y(t) f'(r)}{r},z''(t)=\frac {z(t) f'(r)}{r}\right \} \] ✓ Mathematica : cpu = 0.0075697 (sec), leaf count = 137
\[\left \{\left \{x(t)\to c_1 e^{-\frac {t \sqrt {f'(r)}}{\sqrt {r}}}+c_2 e^{\frac {t \sqrt {f'(r)}}{\sqrt {r}}},y(t)\to c_3 e^{-\frac {t \sqrt {f'(r)}}{\sqrt {r}}}+c_4 e^{\frac {t \sqrt {f'(r)}}{\sqrt {r}}},z(t)\to c_5 e^{-\frac {t \sqrt {f'(r)}}{\sqrt {r}}}+c_6 e^{\frac {t \sqrt {f'(r)}}{\sqrt {r}}}\right \}\right \}\] ✓ Maple : cpu = 0.211 (sec), leaf count = 101
\[\left \{\left \{x \left (t \right ) = c_{5} {\mathrm e}^{\frac {t \sqrt {\frac {d}{d r}F \left (r \right )}}{\sqrt {r}}}+c_{6} {\mathrm e}^{-\frac {t \sqrt {\frac {d}{d r}F \left (r \right )}}{\sqrt {r}}}, y \left (t \right ) = c_{3} {\mathrm e}^{\frac {t \sqrt {\frac {d}{d r}F \left (r \right )}}{\sqrt {r}}}+c_{4} {\mathrm e}^{-\frac {t \sqrt {\frac {d}{d r}F \left (r \right )}}{\sqrt {r}}}, z \left (t \right ) = c_{1} {\mathrm e}^{\frac {t \sqrt {\frac {d}{d r}F \left (r \right )}}{\sqrt {r}}}+c_{2} {\mathrm e}^{-\frac {t \sqrt {\frac {d}{d r}F \left (r \right )}}{\sqrt {r}}}\right \}\right \}\]