1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 2nd Order nonhomogeneous ODE using Undetermined Coefficients

  1. Aug 4, 2009 #1
    1. The problem statement, all variables and given/known data

    Find General Solution:

    2. Relevant equations

    3. The attempt at a solution

    I know you have yh which is the general solution to the left side of the equation set to 0 and then fine the particular solution.

    When i try to find yp1 I get yp1=Ae-3x, y'p1=-3Ae-3x, and y"p1=9Ae-3x

    Substituting that into the left side we get
    Canceling out Ae-3x we get

    SO does this mean when i'm finding the general solution y=yh+yp1+yp2 that yp1 is gonna be 0?

    I Know this is a very simple question but my mind is running in circles!
  2. jcsd
  3. Aug 4, 2009 #2


    User Avatar
    Homework Helper

    roots of the characteristic polynomial are -3 and -2, so your PI for the e-3x is not Ae-3x but Axe-3x, the PI for -27x2 is Bx2+Cx+D, so combining those two, your PI would be

    [tex]y_{PI} = Axe^{-3x}(Bx^2+Cx+D)[/tex]
  4. Aug 4, 2009 #3
    The characteristic polynomial being the left side of the equation?

    Isn't it a double root -3? (y+3)2?
  5. Aug 4, 2009 #4


    Staff: Mentor

    No, -2 is not a root of the characteristic equation. The only root is -3, and this is a double root.
  6. Aug 4, 2009 #5


    User Avatar
    Homework Helper

    oh right it is, I did that wrong in my head...in that case, Axe-3x would be Ax2e-3x
  7. Aug 4, 2009 #6


    Staff: Mentor


    Your solution to the homogeneous equation is yh = Ae-3x + Bxe-3x.

    The particular solution to the nonhomogeneous problem is yp = Cx2e-3x + D + Ex + Fx2.

    The general solution is y = yh + yp.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook