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Inhomogeneous diff. eq.

  1. Oct 4, 2007 #1
    y''+4y = x*sin2x

    Find a particular solution using the method of undetermined coefficients.
    ---------------------------------------------------------------------

    No idea what to do here. My table has no suggestion for a particular solution when r(x) = x*sin2x.
     
  2. jcsd
  3. Oct 4, 2007 #2

    rock.freak667

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    The RHS consists of the product of a Polynomial of degree one and a trig function

    so the P.I. would be (P.I.of the polynomial)*(P.I. for the trig function)
     
  4. Oct 5, 2007 #3

    HallsofIvy

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    You don't learn mathematics by using tables, you learn mathematics by using concepts. For sin(2x) on the right hand side your first thought should be Acos(2x)+ Bsin(2x). With "x" you would try Ax+ B. As rockfreak667 said, combine those ideas:
    try y= (Ax+B)sin(2x)+ (Cx+ D)cos(2x)

    HOWEVER, sin(2x) and cos(2x) already satisfy the differential equation! I'm sure you already know what to do in that situation- multiply by x. Try (Ax2+ Bx)sin(2x)+ (Cx2+ Dx)cos(2x).

    I suspect that, since the equation only involves "even" derivatives, you don't need all of those coefficients- some will be 0- but I see no good way to figure out which in advance.
     
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