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

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In summary, the conversation discusses missing steps to re-write an equation into one with just two terms. The equation in question involves a wave equation hybrid and the term u_{rr}+\frac{2}{r}u_r. After some speculation and attempts at solving, the solution is found by multiplying both sides by r^2.
  • #1
member 428835

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

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

1. What is a PDE?

A PDE, or partial differential equation, is a mathematical equation that involves multiple variables and their partial derivatives. It is used to describe relationships between quantities that vary continuously over a space.

2. Why is it important to re-write the PDE homework statement?

Re-writing the PDE homework statement can help to simplify the equation and make it easier to solve. It can also help to identify any errors or inconsistencies in the original statement and make the problem more manageable.

3. What is a two-term equation solution?

A two-term equation solution is a solution to a PDE that involves only two terms, typically a function and its partial derivative. It is commonly used in engineering and physics to model physical phenomena.

4. How do you approach re-writing a PDE homework statement?

The first step in re-writing a PDE homework statement is to identify the variables and their partial derivatives. Then, simplify the equation by combining like terms and using algebraic manipulations. Finally, check for any errors or inconsistencies and make sure the equation is in its simplest form.

5. Are there any tips for solving two-term equation solutions?

One tip for solving two-term equation solutions is to first separate the equation into two parts, one for the function and one for its partial derivative. Then, solve each part separately and combine the solutions to find the final solution. It is also important to carefully check for any boundary conditions or special cases that may affect the solution.

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