I'm looking for a solution to this set of complicated differential equations:
$$\begin{align} \dfrac{dθ}{ds} & = \dfrac{\cos θ}{r} − z\\ \dfrac{dz}{ds}& = − \cos θ \\ \dfrac{dr}{ds} &= \sin θ \end{align}$$
Ideally, the solutions would be in the forms $θ(s)$, $z(s)$, and $r(s)$.
Does such a solution exist? If so, what is it?