What is a reasonable manufactured solution to test the following equation against its finite difference approximation? I want it to look like a Cosine function about $0$, rotated about $Z$ axis (basically not varying about $\theta$) such that $f$ turns out to be a not so bad function in terms of $r,\theta$
$$u_{rr} \;+\; \frac{1}{r} u_r \;+\; \frac{1}{r^2} u_{\theta\theta}\;+\; Cu \;=\; f(r,\theta)$$