$\displaystyle \frac{\mathrm{d}r}{0}=\frac{\mathrm{d}z}{C}=\frac{ \mathrm{d}u}{0}=\frac{\mathrm{d}v}{0}=\frac{d \Theta}{0}$, where C is a constant.
I gained it via the solution of a linear partial differential equation and $\displaystyle \Theta=\Theta(r,z),\ u=u(r,z),\ v=v(r,z)$.
From the first equality $\displaystyle 0 \mathrm{d} z=C \mathrm{d} r \implies r=k_1$. Similarly, $\displaystyle 0 \mathrm{d} z=C \mathrm{d} u \implies u=k_2$, etc. So the general solution is $\displaystyle u=u(r),\ v=v(r),\ \Theta=\Theta(r).$