1. Not finding help here? Sign up for a free 30min 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!

Differential Equations

  1. Jan 7, 2006 #1
    Solve :

    [tex]y'' + y' - 12y = 4x^2[/tex]
    The complementary equation I get is [tex] y1 = C1 e^3x + C2 e^-4x [/tex]

    But how to solve for the trial solution?
    I do it in this way:

    [tex] f(x) = 4x^2 [/tex]
    [tex] y2 = D (Ax^2 + Bx + C )[/tex]......
    What I want to know is whether my y2 is correct.
     
    Last edited: Jan 7, 2006
  2. jcsd
  3. Jan 8, 2006 #2

    Tide

    User Avatar
    Science Advisor
    Homework Helper

    Are you familiar with the method of variation of parameters?
     
  4. Jan 8, 2006 #3

    TD

    User Avatar
    Homework Helper

    You can certainly use undetermined coefficients since your RHS is just a polynomial. Since its degree is 2, your suggestion for a solution should be a general second degree polynomial as well.

    Your y2 is fine, but it can be simplified a bit, the D isn't necessary. If you would work it out, you'd get ADx²+BDx+CD where 'AD', 'BD' and 'CD' are again just 3 constants so just using A, B and C is fine - then you have the most general second degree polynomial.

    Find its first and second derivative, plug it into your DE and identify coefficients to solve for A, B and C :smile:
     
  5. Jan 8, 2006 #4
    i think you should try variation of parameters as tide suggested
     
  6. Jan 8, 2006 #5
    What is variation of parameters??
     
  7. Jan 8, 2006 #6

    TD

    User Avatar
    Homework Helper

    You can google it, the method is described well in this pdf file.
    This is certainly a method worth learning since it applies more generally than the method of undetermined coefficients (which only works for a limited number of RHS functions)

    Just as a note: your method (undetermined coefficients) will work here as well!
     
  8. Jan 8, 2006 #7
    Thanks a lot.
     
  9. Jan 8, 2006 #8

    TD

    User Avatar
    Homework Helper

    You're welcome, don't hesitate to ask for help if you're stuck :smile:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Differential Equations
  1. Differential equations (Replies: 1)

  2. Differential equation (Replies: 4)

  3. Differential Equation (Replies: 12)

  4. Differential Equations (Replies: 1)

Loading...