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Homework Help: Very simple diff eq [concept help needed for exam]

  1. Mar 22, 2007 #1
    1. The problem statement, all variables and given/known data

    Find the exact solution to this problem
    y'=4x–y+9;y(0)=6


    3. The attempt at a solution

    I am panicing because I have an exam tomorrow and I can't remeber a lot of the basics for diff eq. I tried to solve this using 2nd order style...

    first I made it

    y'-y=4x+9

    For natural solution i do
    r+1=0
    r=-1

    natural solution = A*e^(-x)

    How do I get the forced soution?


    And how would I do it on a second order equation so like

    y''+By'+y = some x terms

    I know how to do natural solutions... its the forced that keeps getting me
     
  2. jcsd
  3. Mar 22, 2007 #2
    You do realize that that is a first order differential equation right? Do you know the standard method of integrating factors for finding the solution of a first order differential equation?
     
  4. Mar 22, 2007 #3
    I am trying to avoid first order methods, I would like to be able to solve it using second order method... since r is a real root it would take the natural form A*e(-rx)

    Really I guess I picked a bad example... I thought it would be easier than second order... I am trying to figure out how to solve for a second order "forced solution"
     
  5. Mar 22, 2007 #4
    Why are you trying to avoid first order methods for a first order equation? It really is easiest to just find an integrating factor and solve the equation that way.
     
  6. Mar 22, 2007 #5
    I know its the easiest way, but I don't have any first order problems on my upcomming exam, I just thought it would be easier to learn how to do forced solutions on a first order problem (which I don't even know if it is possilbe) I know how to do the integrating factor method.
     
  7. Mar 22, 2007 #6

    SGT

    User Avatar

    If your forcing function is a polynomial, the particular solution will be a polynomial of the same degree. In your case
    [tex]y_p = Ax + B[/tex]
    Substitute [tex]y_p[/tex] and its derivative in the differential equation to obtain the parameters A and B.
     
    Last edited by a moderator: Mar 22, 2007
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