R help - Apr 2012 - How to find eigenfunctions and eigenvalues of a fourth order ODE

Dear all,

I am having trouble with the following problem. Suppose we have the fourth
order ODE with boundary conditions:

http://r.789695.n4.nabble.com/file/n4591748/problem.jpg problem.jpg 

where q(t) is a known function.

Note here the lambda parameter is changing, so essentially we have a series
of ODEs. lambda is called an eigenvalue, the solution y is called an
eigenfunction associated with lambda. The question is to find the
eigenvalues lambda and eigenfunctions y. 

In matlab, this can be done. I am wondering if R has similar functions to
achieve this goal. Any suggestions will be highly appreciated. 

Best regards,
Jeff

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