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Thread: Initial value problem: stuck on detail, help wanted!

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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 $\displaystyle V(t)$, when: $\displaystyle k = 0$, and also
    $\displaystyle k != 0$.

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

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

    This is what I've got so far:


    $\displaystyle V'' + 2V' + V = 0$


    $\displaystyle (m+1)(m+1)$


    $\displaystyle m1 = m2 = -1$

    so homogenous eqn is:

    $\displaystyle u = A1.exp(-x) + A2.x.exp(-x)$

    and non-homog. one is:

    $\displaystyle y = B1.exp(-kt) + B2.sin(t) + B3.cos(t)$
    Last edited by dan569; Nov 11th 2008 at 08:51 AM. Reason: fixing formatting
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