In a Differential Equation how is the forcing function and the solution to the DE related? Does the forcing function die off and the solution continues to oscillate?

(this all may be incorrect, I don't know)

Question

In a Differential Equation how is the forcing function and the solution to the DE related? Does the forcing function die off and the solution continues to oscillate?

(this all may be incorrect, I don't know)

anonymous · Answer

You can solve the related homogeneous DE to see what the solution without the forcing function looks like.  And then the full DE to see the effect of the forcing func. In general solutions are written as a super position of the homogeneous solution and a particular (forced) solution.

anonymous · Answer

As for continued oscillations, that is equation specific, some DE's will reach equilibrium as t -> infinity and some won't.