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2nd order differential equation

  1. Aug 4, 2011 #1
    1. The problem statement, all variables and given/known data

    y''+16y=3.36

    This is actually part of a spring question I'm attempting at the moment, and I'm having a mental blank on how to deal with the 3.36.


    2. Relevant equations

    n/a



    3. The attempt at a solution

    I've found the characteristic equation and solution based from that;
    [tex] c_1 cos(4x) + c_2 sin(4x) [/tex]
    but the answer is
    [tex] c_1 cos(4x) + c_2 sin(4x) + 0.21 [/tex]
     
    Last edited: Aug 4, 2011
  2. jcsd
  3. Aug 4, 2011 #2

    SteamKing

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    Remember: The general solution to any linear non-homogeneous differential eq. is equal to the soln. to the homogeneous sq. plus the particular soln. to the non-homogeneous eq.
    What is your characteristic eq. here?
     
  4. Aug 4, 2011 #3

    vela

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    You found the homogeneous solution. You need to find the particular solution. Try substituting a trial solution of the form yp=A and solving for A.
     
  5. Aug 4, 2011 #4
    [tex] y_p = A [tex]
    so doing that I get A = 0.21, which gives me the correct solution.

    thanks.
     
  6. Aug 4, 2011 #5
    However do you know the rationale for choosing trail function as A instead of A x
     
  7. Aug 4, 2011 #6
    yep. so it isn't a multiple of the homogenous solution. I did a course of DE's a while ago, I just forgot what to do in this case.
     
  8. Aug 4, 2011 #7

    HallsofIvy

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    If you had tried Ax, then (Ax)''= 0 so the equation would have been 16Ax= 3.36. The left side has an "x" and the right side doesn't. May I ask why you are doing this problem? I would imagine it is because you are taking a course in differential equations but I cannot imagine you having a homework problem like this if you are not in a chapter of your textbook that has a detailed description of "Undetermined Coefficients" as this method is called.
     
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