Differential equation - delta function

[Teri]

Moved from technical math section, so is missing the homework template.
How to solve this equation please?
I found charakteristic roots ia $\pm \sqrt{-a^{-k^2}}$. Thank you
Moderator note: Edited the LaTeX above to show the exponent correctly.

 

[ChrisVer]

Do you know why you derive the characteristic equation and try to find its roots?
Also, the solutions you give look weird, redo the solution of the characteristic equation.
Is the delta you have in the RHS a constant term or the delta-function ?

 

[Mark44]

I found charakteristic roots ia $\pm \sqrt{-a^{-k^2}}$.

I get the roots of the characteristic equation for the homogeneous diff. equation as $r = ia \pm \sqrt{k^2 - a^2}$. It's possible that what you intended was something like this. If so, you had some errors.

Also, questions such as this one should be posted in the Homework & Coursework section, not in the technical math sections, and should use the homework template. I have moved the thread to the appropriate section.

Is the delta you have in the RHS a constant term or the delta-function ?

Based on the thread title, it appears that what is meant is the Dirac delta function.