I am having trouble understanding how to use Fourier transforms to solve ODEs and came across this problem in some exercises from the text I am learning from:
Use Fourier transforms to solve $-u_{xx}+a^2u=\delta$ where $\delta=\delta(x)$ is the Dirac delta function.
I would appreciate if someone could help me solve this and could provide some general outline on how to solve DEs like these with Fourier transforms. Thanks.