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I'm working on a question which has lead me to the Laplace equation in cylindrical coordinates. I've looked it up and found that, for the radial component, this is equivalent to

$$\nabla^2\ f = \frac{1}{r} \frac{\partial}{\partial r}\left(r \frac{\partial f}{\partial r}\right) = 0.$$

I think I should be able to separate this out somehow to get something like the form

$$a\frac{\partial f}{\partial r}+b\frac{\partial^2 f}{\partial r^2} =0.$$

Any ideas? I hope I've made this clear enough!

Davide Giraudo
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Jean
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1 Answers1

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If you know how to differentiate a product, then $$ \frac{\partial}{\partial r} \left( r \frac{\partial f}{\partial r} \right) = \frac{\partial f}{\partial r} + r \frac{\partial^2 f}{\partial r^2}. $$

Siminore
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