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Homework Help: How to solve the ODE y'' + y = sin(x)

  1. Jul 12, 2009 #1
    1. The problem statement, all variables and given/known data

    initial conditions: y(90 deg) = 3, y(45 deg) = 2

    Calculate y at x = -1

    2. Relevant equations

    3. The attempt at a solution

    I have gotten the following:

    r^2 + 1 = 0 Therefore, r1=i and r2 = -i

    u=(c1)cosx + (c2)sinx

    v=Asinx + Bcosx
    v'=Acosx - Bsinx
    v"=-Asinx - Bcosx

    -Asinx -Bcosx + Asinx + Bcosx - sinx = 0

    everything cancels down to: -sinx = 0. Thus, v=0

    Then I get,

    y=(c1)cosx + (c2)sinx + 0

    y(45 deg) shows that c2=2

    y(90 deg) shows that c1=3

    Thus, y=3cosx + 2sinx

    y(-1) = -.06204

    Could someone please let me know where I am making a mistake?

    Thank you in advance!
  2. jcsd
  3. Jul 12, 2009 #2
    Re: Differential

    The solution of the homogeneous case has terms cos x and sin x in it. The right-hand-side *also* has one of those terms in it. Presumably your textbook has the information of what to do in this exceptional case... as you found, the usual method does not work.
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