Whoa. WolframAlpha gave this intimidating answer. The Mathieu cosine and sine functions appear to be the solutions to this DE. Not very pretty, I'm afraid. And I don't know much more than what I've just written. What class is this for, anyway?

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- Sep 1st 2010, 11:46 AM #1

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- Sep 1st 2010, 12:45 PM #2
Whoa. WolframAlpha gave this intimidating answer. The Mathieu cosine and sine functions appear to be the solutions to this DE. Not very pretty, I'm afraid. And I don't know much more than what I've just written. What class is this for, anyway?

- Sep 2nd 2010, 02:05 PM #3
The DE is linear and 'incomplete' and its general solution is...

(1)

... where and are respectively an 'even' and an 'odd' function that we suppose analytic so that is...

(2)

Let's consider first , for which we can hypothesize that is . Is...

(3)

... and remembering that is...

(4)

... we arrive to write...

(5)

Combining (3), (5) and the DE we are able to find the ...

... so that is...

(6)

To be continued in succesive post...

Kind regards

- Sep 2nd 2010, 05:31 PM #4
Regarding the 'odd function' we proceed as the and obtain...

(1)

... and...

(2)

Now from (1), (2) and the DE we obtain the as follows...

... so that is...

(3)

The conclusion is that the DE...

(4)

... has general solution...

(5)

... where and have been found in the previous and in the actual post...

Kind regards