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5th order DE with g(x)=32exp^(2x)

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

    Use variations of parameters to find the general solutions of the following differential equations.

    y'''''-4y'''=32exp^(2x)

    2. Relevant equations

    no relevant equations.

    3. The attempt at a solution

    hey there, I tried solving this question. I got the homogeneous equation.

    yh(x)=C1+C2x+C3X2+C4exp^(2x)+C5exp^(-2x)

    but after this step.. I am stuck..

    Because I am not quite sure whether I am in the correct path to look for the general solutions. After I have this equation, I did the wronskian matrix, I found the determinant of the 5X5 matrix is 512. Am I correct? Please correct me if I am not in the journey to my answer.

    Besides that , If I were to use the variations of parameters. The matrix would be 5X5 dimensions. Is it correct?

    Thanks


    edited due to duplication on the template question.. sorry..
     
  2. jcsd
  3. Feb 5, 2009 #2
    You should get into the habit of reducing such a DE into something more familar. Let [tex]u=y^{(3)}[/tex], so the DE becomes [tex]u'' - 4u = 32e^{2x}[/tex].

    Proceed as usual (involves a 2x2 matrix) to solve for u(x). Then you can obtain y(x).
     
  4. Feb 5, 2009 #3
    hey there.
    thanks alot for the reply..

    i will try out your attempt.. then i will post if i need anymore help..
    thanks
     
  5. Feb 5, 2009 #4
    hey there, i have tried out your attempt.. but I only can find the general solutions

    the wronskians i found was -4, am I in the right path ?

    u(x) = uh(x) + up(x) = C1e2x+C2e-2x+8xe2x-2e2x

    how should I convert it to y(x) = yh(x) + yp(x)

    If i use the equation u gave me u = y(3). Am I suppose to integrate u(x) by 3 times?


    any clue for me?

    thanks
     
    Last edited: Feb 5, 2009
  6. Feb 5, 2009 #5
    Well done!

    No need; you've done the variation of parameters work for u.

    Exactly!
     
  7. Feb 5, 2009 #6
    Wow.. thanks alot.. I think I will post the proper solutions after I finished the steps ok ?

    and I will let you go through my answer to see whether I did any mistakes.. Thanks
     
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