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NonHomogeneous Equations and Undetermined Coefficients

  1. Feb 22, 2009 #1
    NonHomogeneous Equations and Undetermined Coefficients

    Find the particular solution;

    y''-10y'+25y=-18e^(5t)

    here is my work

    yp(x)=-Ae^(5t)
    yp'(x)=-5Ae^(5t)
    yp''(x)=-25Ae^(5t)

    plug into equation

    [-25Ae^(5t)]-10[-5Ae^(5t)]+25[-Ae^(5t)...

    Now; I have 0=-18e^(5t) which doesnt make sense.

    Thank You
     
  2. jcsd
  3. Feb 22, 2009 #2

    Mark44

    Staff: Mentor

    Why did you use -Ae^(5t) as your particular solution? That is, with the negative sign?

    The particular solution you chose happens to be a solution to the homogeneous equation y''-10y'+25y = 0.

    The characteristic equation for the homogeneous equation is r^2 - 10r + 25 = 0, and there is a repeated root for r = 5. This means that in addition to Ae^(5t), Bte^(5t) will also be a solution to the homogeneous equation.

    For your equation, I would try y = Ct2e5t as a particular solution.
     
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