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Math Help - Initial value problem: stuck on detail, help wanted!

  1. #1
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    Smile Initial value problem: stuck on detail, help wanted!

    Hi there.

    I'm stuck solving the following problem, as I'm not sure how to find the values of 'B'. I gather I need to use the original DE, but I'm lost as to how. Can someone please help me out?

    Any help would be greatly appreciated.
    --------------------------------------------------------------------------
    Find V(t), when: k = 0, and also
    k != 0.

    initial conditions are: V(0) = 0 and V'(0) = 0

    (d^2V/dt^2) + 2 (dV/dt) + V = Vo ( exp(-kt) + 7ksin(t) )
    --------------------------------------------------------------------------

    This is what I've got so far:


    V''  +  2V'  +  V = 0


    (m+1)(m+1)


    m1 = m2 =   -1

    so homogenous eqn is:

    u = A1.exp(-x) + A2.x.exp(-x)

    and non-homog. one is:

    y = B1.exp(-kt) + B2.sin(t) + B3.cos(t)
    Last edited by dan569; November 11th 2008 at 09:51 AM. Reason: fixing formatting
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