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Math Help - need some help setting up a few problems

  1. #1
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    need some help setting up a few problems

    Here are the problems I am having difficulty with:


    1.
    Given the characteristic equation of a 4th order differential equation has repeated roots of i and - i,
    a) write the general solution of the differential equation
    b)write the original differential equation


    2.
    (x-2)y'' + (x-1)y' + 4y = 0
    a) write the general solution near x = 0.
    b) find the indicial equation and the exponents at the singularity.


    Those are the 2 problems I am having trouble with. Its all just on how to start.. Here is what im am doing for each of them:

    1.[/B]
    A. I dont know how to do....
    B.
    (m^2+2m+1)(m^2+2m+1)
    y^(^4^) +4y''' + 6y'' + 4y' + 1 = 0



    2.
    With this you can just substitute
     \sum Cn X^n
    where n = 0 to infinity and its appropriate derivatives. correct?
    Last edited by Jeonsah; May 15th 2011 at 09:36 PM.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by Jeonsah View Post
    1.Given the characteristic equation of a 4th order differential equation has repeated roots of i and - i,
    a) write the general solution of the differential equation
    b)write the original differential equation

    If a\pm bi\;(b\neq 0) are roots of the characteristic equation with multiplicity 2, choose

    e^{at}\cos t,\;e^{at}\sin bt,\;te^{at}\cos t,\;te^{at}\sin bt

    to form a basis of the solution space.
    Last edited by FernandoRevilla; May 16th 2011 at 12:37 AM.
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