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Homework Help: Diff Eq Undetermined Coefficients

  1. Jun 1, 2007 #1
    1. The problem statement, all variables and given/known data
    Find the solution for y"+2y'+5y=(e^x)sinx

    2. Relevant equations

    3. The attempt at a solution

    So far I think I've gotten the solution from the characteristic equation, but I'm having trouble with the particular solution.

    For the characteristic equation solution:
    Using the quadratic formula r= -1(+/-)2i
    So y=(e^-x)((C1)cos(2x)+(C2)sin(2x)

    For the particular solution I think I'm assuming correctly that y=A(e^x)sin(2x)+B(e^x)cos(2x), or am I not catching a term that can be combined with the complementary solution? Or am I just using the wrong equation all together?
  2. jcsd
  3. Jun 1, 2007 #2


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    Homework Helper
    Gold Member

    In this line: y=A(e^x)sin(2x)+B(e^x)cos(2x), you shouldn't have the 2's inside the trig arguments. Since the RHS of the problem statement has only a sin(x), your "guess" should only include trig functions with x as the argument. You are getting the 2's from the Homogeneous Solution, but in this problem, the H solution, does not affect your "guess" of the particular solution.
  4. Jun 1, 2007 #3
    Thanks! I don't know how I overlooked that.
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