1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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!

Why doesn't this method work? (Re: Simultaneous ODEs)

  1. May 10, 2010 #1
    I have been working on a derivation in which the following simultateous ordinary differential equations have appeared:
    [tex] f^{(4)}(x)-2 a^2 f''(x)+a^4 f(x)+b(g''(x)-a^2 g(x))=0,[/tex]
    [tex] g^{(4)}(x)-2 a^2 g''(x)+a^4 g(x)-b(f''(x)-a^2 f(x))=0,[/tex]
    where [tex]a[/tex] and [tex]b[/tex] are constants. I figured that I could solve this using Fourier transforms. First, I transform the above, using [tex]\nu[/tex] as the transform space analogue of [tex]x[/tex], into the following:
    [tex] (\nu^2 +a^2 )\hat f(\nu ) -b \hat g(\nu )=0,[/tex]
    [tex] (\nu^2 +a^2 )\hat g(\nu ) +b \hat f(\nu )=0.[/tex]
    I then rearrange these equations via substitution into
    [tex] [(\nu^2 +a^2 )^2 +b^2 ] \hat f(\nu ) =0,[/tex]
    [tex] [(\nu^2 +a^2 )^2 +b^2 ] \hat g(\nu )=0.[/tex]
    Taking the inverse Fourier transform then results in
    [tex] f^{(4)}(x)-2a^2 f''(x)+(a^4 +b^2 )f(x)=0,[/tex]
    [tex] g^{(4)}(x)-2a^2 g''(x)+(a^4 +b^2 )g(x)=0.[/tex]

    However, after I solve for these two ODEs using the boundary conditions, I find that the resulting answer is erroneous. I can only conclude that the above methodoly doesn't work, although I can't see why.

    Could anyone point out the mathematical error in the above steps?
    Last edited: May 10, 2010
  2. jcsd
  3. May 10, 2010 #2


    User Avatar
    Homework Helper

    can you show your transform... shouldn't you get factors of [itex]nu^4[/itex]?
    Last edited: May 10, 2010
  4. May 10, 2010 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    The OP is dividing out a common factor of [itex]\nu^2+a^2[/itex].
  5. May 13, 2010 #4
    Yes, that's what I've done.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook