I have been working on a derivation in which the following simultateous ordinary differential equations have appeared:(adsbygoogle = window.adsbygoogle || []).push({});

[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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

**Physics Forums | Science Articles, Homework Help, Discussion**