I know I should know this... it looks so ridiculously easy. In the course of getting d'Alembert's wave equation solution, we get the following equation:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]2cp'\left(x\right)=cf'\left(x\right)+g\left(x\right)[/tex]

The primes are derivatives wrt t. Then we re-order the equation and "integrate the relation" to get an expression for p:

[tex]p\left(\xi\right)=\frac{1}{2}f\left(\xi\right)+\frac{1}{2c}\int^{\xi}_{0}g\left(s\right)ds[/tex]

I have to be missing something very, very simple. How can I differentiate [tex]p\left(x\right)[/tex] wrt [tex]t[/tex] then integrate wrt something (x, I suppose, in this case) and recover the original function p? Or am I NOT recovering it... just something new named [tex]p\left(\xi\right)[/tex]? Thanks for the help!

Tom

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# Help With Partial Differentiation & Integration

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