1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Inhomogeneous diff EQ, undetermined coefficients

  1. Mar 4, 2010 #1
    Find the solution of:

    y" + 3y' = 72sin(3t) + 36cos(3t)
    where y(0) = 6 and y'(0) = 9

    I first found the solution to the homogeneous eq:

    the roots (R^2 + 3R = 0) are R = 0, -3
    which gives the family of solutions:
    y = a(1) + be^(-3t)
    and y' = -3be^(-3t)

    using the initial conditions (maybe Im not supposed to use them here?)
    I find a = 9, b = -3

    For the inhomogeneous eq:

    I try (guess)
    y = Asin(3t) + Bsin(3t)
    y' = 3Acos(3t) - 3Bsin(3t)
    y" = -9Asin(3t) - 9Bcos(3t)

    substitute those values into the original equation (left hand side) I find

    sin3t(-9A-9B) + cos3t(-9B-9A) = 72sin3t + 36cos3t

    therefore
    -9A - 9B = 72
    -9B - 9A = 36
    giving B = -6, A = -2


    Therefore I get the solution:

    y = 9 - 3e^(-3t) - 2sin3t - 6cos3t

    What did I do wrong (this answer is incorrect)
    Thanks
     
  2. jcsd
  3. Mar 4, 2010 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi offbeatjumi! :smile:
    But y(0) ≠ 6, is it?

    So you did need to wait until the end before finding the constants. :wink:
     
  4. Mar 4, 2010 #3
    thank you! i wasn't sure about where to apply initial conditions
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Inhomogeneous diff EQ, undetermined coefficients
Loading...