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Lost on eigenvalues

  1. Nov 20, 2004 #1
    I'm having trouble getting started on this problem... I just really don't understand what to do.

    [tex]X'+2X'+(\lambda-\alpha)X=0, 0<x<1[/tex]

    a. Is [tex]\lambda=1+\alpha[/tex] an eigenvalue? What is the corresponding eigenfunction?
    b. Find the equation that the other eigenvalues satisfy.

    I appreciate any help you can give me!

    Last edited: Nov 20, 2004
  2. jcsd
  3. Nov 20, 2004 #2
    are u sure that the edo is correct?

    you have there a linear second order d.o with constant coeficients and initial values, so your solution will be some linear comb. of exp[rt] (you have to calculate r of course).

    i dont really understand why would you end with an eigenvalue problem in this way but maybe im not well informed.
  4. Nov 21, 2004 #3
    Yeah, everything on there is correct. I'm not sure what you mean though...

    nm... figured it out.
    Last edited: Nov 22, 2004
  5. Nov 22, 2004 #4

    let [itex]X=e^{rt}[/itex] implies






    so [itex]A=-B[/tex]


    [itex]A=0[/itex] would lead to the trivial solution, so


    [itex]\lambda=1+\alpha[/itex] is clearly an eigenvalue

    and [itex]\lambda_{m}[/itex] satisfy the equation

    Last edited: Nov 22, 2004
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