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Help with solving a IH equation

  1. Oct 24, 2009 #1
    1. The problem statement, all variables and given/known data

    d2i/dt2 + 6di/dt + 25i = -292sin4t

    2. Relevant equations

    3. The attempt at a solution

    i got a solution of
    Ae^(-3t)cos4t + Be^(-3t)sin4t + 292/9(cos4t) + 146/9(sin4t)
    want to know if im right
    Last edited: Oct 24, 2009
  2. jcsd
  3. Oct 24, 2009 #2


    Staff: Mentor

    Your solution looks reasonable. Your solution can be divided into two parts: the solution to the homogeneous equation i'' + 6i' + 25i = 0, and the particular solution to the nonhomogeneous equation you have.

    So your general solution is i(t) = ih(t) + ip(t), where ih(t) consists of the first two terms of your solution, and ip(t) consists of the last two terms.

    Your homogeneous solution checks with what I got. To confirm that your general solution is correct, all you need to do is check that your particular solution actually works.

    From ip(t) = (292/9)cos4t + (146/9)sin4t, calculate ip' and ip''. If ip'' + 6ip' + 25ip equals -292sin4t, your solution is correct.
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