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Question about differential equations?(Nonhomogeneous equation)

  1. Feb 27, 2009 #1
    I am having trouble with the following
    Nonhomogeneous equation

    y''+7y'+10y=18te^(5t)

    yp(t)=Ae^(2t)+Bte^(5t)
    yp'(t)=5Ae^(5t)+Be^(5t)+5Bte^(5t)
    yp''(t)=25Ae^(5t)+5Be^(5t)+5Be^(5t)+25...
    A=(-4.37/70), B=(18/70)
    i plugged into yp and got
    (-4.37/70)e^(2t)+(18/70)te^(2t)

    But it was wrong


    Thank You
     
  2. jcsd
  3. Feb 28, 2009 #2

    Mark44

    Staff: Mentor

    Why did you try Ae^(2t) as a part of your particular solution?

    The solutions to the homogeneous equation are c1e^(-2t) and c2e^(-5t), and this can be seen by looking at the characteristic equation for the homogeneous differential equation. For the nonhomogeneous equation, any particular solution must be of the form Ae^(5t) + Bte^(5t).
     
  4. Feb 28, 2009 #3
    oops sorry, that was just a typo, i meant to put e^(5t) not e^(2t)
     
  5. Feb 28, 2009 #4

    Mark44

    Staff: Mentor

    OK, I didn't catch what you had in the following lines. That particular solution should work, but check your work to make sure that you did the derivatives correctly, and don't use approximate values (e.g., -4.37/70 for A).

    Also, you apparently substituted your values for A and B into the incorrect particular solution.
     
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