Math Is Fun Forum

mrpace

Member

Registered: 2012-08-16

Posts: 88

Differential Equations help please

Find all the real eigenvalues and eigenfunctions for the eigenvalue problems

y'' + λy = 0,
y(-3) = y(3),
y '(-3) = y '(3).

Not really sure on the process. Thanks for any help.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,158

Re: Differential Equations help please

hi mrpace,

Not really my area so I've been waiting for someone else to have a go at this.  But no one has so I'll give you my thoughts.  Maybe this will attract someone else to do it properly   .

To solve second order differential equations like this you are suppose to look at the 'equivalent' quadratic ... in this case

To get real solutions, you'd want lambda to be negative, so let's say

Then a solution is

and another one is

I think, and this is where I'm getting 'shaky', this means the general solution is:

where A and B are constants.  This certainly does fit the differential equation OK.

So then you put in the boundary conditions to find A and B.  Maybe I made a mistake, but so far that has just given me nonsense.

I'll start again on a fresh sheet of paper and see if I can convert this into sense. 

LATER EDIT:

here's a typical graph:

This obeys the first constraint but won't simultaneously obey the second. 

Or is this two separate questions in one?

Bob

Last edited by Bob (2015-03-22 00:57:53)

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