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4th order homogeneous linear ODE with constant coefficients

  1. Aug 4, 2009 #1
    Can someone explain to to me how to find the general solution of the fourth order ODE

    y''''-y''=0

    Right now I have

    y(x)=a+b*x+c*e^-x+d*e^x

    where a,b,c and d are constants.

    Not sure if this is correct just wanted to double check.
     
  2. jcsd
  3. Aug 4, 2009 #2
    Seems right to me at first glance. Your r values for the aux. eq. are correct and that's about all the problem comes down to since it is set equal to 0 and not a constant or another function which would lead to undetermined coefficients.
     
  4. Aug 5, 2009 #3

    Mute

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    Yes, it's correct. Another way you can check is to note that if you set u = y'', you get

    u'' - u = 0,

    an equation which you pressumably know the solution to. It's then just a matter of integrating twice.
     
  5. Apr 18, 2010 #4
    Re: 4th order homogeneous linear ODE with variable coefficients

    please. anyone can help me to get the general solution of the equation:
    EI(X)Ø'''(X)+Km(x)Ø(x)=0
    where: k= constant
    EI(X) and m(x) are variable coefficients
    and i will be very grateful for him...........
     
  6. Apr 18, 2010 #5
    Re: 4th order homogeneous linear ODE with variable coefficients

    please. anyone can help me to get the general solution of the equation:
    EI(X)Ø'''(X)+Km(x)Ø(x)=0
    where: k= constant
    EI(X) and m(x) are variable coefficients
    and i will be very grateful for him...........
     
  7. Apr 20, 2010 #6
    my colleages....why i didnot answer about my question????????
     
  8. Apr 20, 2010 #7
    sorry, why i didnot find any answer about my question???????
     
  9. Apr 25, 2010 #8
    this may help you. Its something i made for the 1d 4th order wave eqn... i think you will find pg 7 handy.
     

    Attached Files:

  10. Apr 25, 2010 #9
    thank you very much Nick Bruno....But the problem is that, how can find the solution of the equation when EI and m are variable with x-axis and not constants....i think that the equation can be solved by seperation of variables but the resulted equations will be on the form of ODEs with variable coefficients which i am looking for their solutions, and i will be thankful for anybody can help me in this subject...
     
  11. Apr 25, 2010 #10
    looks like you may need to use sturm-liouville and use a computer to solve your problem.
     
  12. May 11, 2010 #11
    Hi colleages, can anyone help me to get this paper which is entitled;"solution of ordinary linear differential equations with variable coefficients by impulsive admittances". this paper in the quarterly journal of mechanics and applied mathematics, volume 6, no.1, pp.122-127. by W.J. Duncan, 1953............please help me to get this paper and i will be very grateful for this...
     
  13. May 11, 2010 #12

    Redbelly98

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    Moderator's note: please ask new questions by creating and posting in a new thread, rather than posting in existing threads. New threads can be created by clicking the "New Topic" [PLAIN]https://www.physicsforums.com/Prime/buttons/newthread.gif [Broken] button.

    You can purchase the paper here:
    http://qjmam.oxfordjournals.org/cgi/reprint/6/1/122

    If you don't want to spend 32 $US, I would look for the journal at the math department library of a local university.
     
    Last edited by a moderator: May 4, 2017
  14. May 12, 2010 #13
    my colleage....i havenot the way to buy this paper, because, i havenot the prepay cards...
    please, if you can to get this paper,send it to me..
     
  15. May 13, 2010 #14

    HallsofIvy

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    Omarxx84, you are coming awfully close to being banned from this forum.

    First, you "hijacked" someone else's thread to ask a completely unrelated question which is very rude. (It's not that hard to click on the "new topic" button on the main menu.)

    Second, you are asking people to send you a copy of a copy-righted paper, which is a crime.
     
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