(Solved): 3. The symbols \( C_{1} \) and \( \mu \) are constants with known values. The differential equatio ...

3. The symbols \( C_{1} \) and \( \mu \) are constants with known values. The differential equation \[ \frac{\mu}{r} \frac{\mathrm{d}}{\mathrm{d} r}\left(r \frac{\mathrm{d} v_{z}(r)}{\mathrm{d} r}\right)=C_{1} \] has the solution \[ v_{z}(r)=\frac{1}{2 \mu} C_{1} \frac{r^{2}}{2}+C_{2} \ln (r)+C_{3} \] where \( C_{2} \) and \( C_{3} \) are constants with unknown values. Question: If the boundary conditions are \( v_{z}\left(r=R_{1}\right)=0 \) and \( v_{z}\left(r=R_{2}\right)=0\left(0