If I solve a simple 2nd order ODE using a Fourier transform, I only get one solution. E.g.:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \frac{d^2f}{dx^2}=\delta [/tex]

[tex] (2\pi ik)^2\tilde{f}=1 [/tex]

[tex] \tilde{f}=\frac{1}{(2\pi ik)^2} [/tex]

[tex] f = \frac{1}{2}xsgn(x) [/tex]

However, the general solution is

[tex] f = \frac{1}{2}xsgn(x) + Cx + D [/tex]

Why do I only get one of the solutions? Are the solutions with C and D non-zero not also valid distributions whose second derivatives are the delta distribution?

**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!

# FT to solve 2nd order ODE; only one solution

Loading...

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