Re-writing the PDE Homework Statement | Two-Term Equation Solution

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SUMMARY

The discussion focuses on re-writing the PDE homework statement involving the equation $$u_{tt} - c^2(u_{rr}+\frac{2}{r}u_r) = 0$$ into a two-term format. Participants explore the relationship of the equation to the wave equation and suggest multiplying both sides by $$r^2$$ as a solution approach. This method simplifies the equation and aids in finding the missing steps required for the homework assignment.

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Homework Statement


Provide the missing steps to re-write the equation into one with just two terms $$u_{tt} - c^2(u_{rr}+\frac{2}{r}u_r) = 0$$

Homework Equations


Nothing, other than this looks similar to the wave equation hybrid. (I'm just speculating)
Also, I'm a little uncertain what is being asked.

The Attempt at a Solution


Well nothing comes to mind. I am looking at this term: ##u_{rr}+{2}u_r/{r}##. So far nothing huge is coming to mind. I initially tried something like ##(u_r/r)'## and then ##(u_r \ln r)'## since they looked close to the above but nothing helps. Any creative ideas out there?

Thanks a ton
 
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Try multiplying both sides by ##r^2##.
 
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Brilliant! Thanks a ton!
 

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