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Separation Into Differential Equations

I would use the entire template except this question is very simple and does not require all of it.

1. Homework Statement
How do I separate
[tex]\frac{X''(x)}{X(x)}[/tex]+[tex]\frac{Y''(y)}{Y(y)}[/tex]=[tex]\sigma[/tex]
into ordinary differential equations when [tex]\sigma[/tex] is a constant.

Thanks for your help!
 

Answers and Replies

You already seem to have seperated the differential equation, because the x-dependence is clearly seperate from the y-dependence.

On the right hand side you have two terms, one depending on x only the other depending on y only. Their sum should not depend on either x or y but should be constant.

Can you conclude HOW the x-dependent term must depend on x in order for the sum of this first term and the only(!) y-dependent second term not to depend on x?

The same for the y-dependence of the second term. Can you figure out HOW it depends on y given the fact that if you add the y-independent first term the result must be y-independent?
 

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