Using separation of variables

Now what?

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- Jan 1st 2011, 06:29 PM #1

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- Jan 1st 2011, 07:04 PM #2
Well, pick a constant of separation:

The first equality gives you a DE for The second equality gives you another equation that, I believe separates out thus:

You can do the same sort of trick you just did. That is, solve for and choose another separation constant.

You follow?

- Jan 1st 2011, 09:25 PM #3

- Jan 1st 2011, 09:36 PM #4

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- Jan 1st 2011, 09:40 PM #5

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This is from Elementary PDE by Berg and McGregor 1966.

...different technique for finding a particular solutions of homogeneous linear PDE is called the method of separation of variables. The exponential solution , are products of functions of the separable variables.... We seek a solution of the form (pg. 14).

- Jan 1st 2011, 11:19 PM #6

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Dear dwsmith,

Think about it like this. You have the two solutions,

--------(Seperation method)

---------(Exponential method)

Consider the exponential part with y as the variable. Since the coefficient of y must be equal in both of these equations,

Now move on to the exponential term with z as the variable. Using the same reasoning,

(1) and (2) gives the substitutions necessary to convert the solution obtained from the seperation method to the solution obtained from the exponential method. Hope you understood.

- Jan 2nd 2011, 01:40 PM #7

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- Jan 2nd 2011, 05:38 PM #8

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- Jan 2nd 2011, 05:42 PM #9

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