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Setting up particular solution for nonhomogenous diff eq'n

  1. Apr 19, 2015 #1
    Given the nonhomogenous differential equation y'' + 3y' + 2y = -10e^(3t), the roots are r = -2 & -1, & the characteristic eq'n is yc(x) = c1e^(-2t) + c2e^(-t)

    How do we go about setting up the particular solution?

    There is no repetition between terms so I know that we do not add a variable to the particular solution. Since we have -10e^3t do we set up the particular solution as yp(t) = -Ae^3t? OR just yp(t) = Ae^3t? I know that A just represents a constant but do I need to include the negative sign or not?

    Thank you.
     
    Last edited by a moderator: Apr 19, 2015
  2. jcsd
  3. Apr 19, 2015 #2

    LCKurtz

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    It doesn't matter whether you use the ##-A## or ##A##. Try them.
     
    Last edited by a moderator: Apr 19, 2015
  4. Apr 19, 2015 #3

    Mark44

    Staff: Mentor

    In future posts, please do not delete the homework template.
     
  5. Apr 19, 2015 #4
    When setting up the particular solution as yp(t) = Ae^(3t), yp'(t) = 3Ae^(3t) and yp''(t) = 9Ae^(3t). After substituting these back into the original diff eq'n we get A = -1/2.

    However, when setting up the particular sol'n as yp(t) = -Ae^(3t), yp'(t) = -3Ae^(3t) and yp''(t) = -9Ae^(3t). After substituting these back into the original diff eq'n we get A = 1/2.

    So, I do believe there is a difference because -1/2 is not equal to 1/2.

    Which substitution should I use, A or -A?
     
  6. Apr 19, 2015 #5
    You mean those 1.

    2.

    3.

    things?
     
  7. Apr 19, 2015 #6

    Mark44

    Staff: Mentor

    Yes, and the sections for Problem Statement, Relevant Equations, and Attempt. Per forum rules, the homework template is required for homework problems.
     
  8. Apr 19, 2015 #7
    Oh, I get it now. -A = 1/2 and A = 1/2 so it doesn't matter... derp.

    Thank you so much!
     
  9. Apr 19, 2015 #8
    Sounds good, I will use them from now on.
     
  10. Apr 19, 2015 #9

    Mark44

    Staff: Mentor

    OK, good. We appreciate it.

    I should mention that there's no point in writing -Ae3t, as A could be positive or negative. All that will come out in the wash when you solve for A.
     
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