Solution
= Solution
The <radially symmetric planar dynamical system> formulas give
$$
\boxed{f(r)=kr^3,\qquad g(\theta)=-1}.
$$
With $r(0)=1$ and $\theta(0)=0$,
$$
\boxed{r(t)=\frac1{\sqrt{1-2kt}}},
\qquad
\boxed{\theta(t)=-t},
$$
again on the maximal interval for which the denominator is positive.