- #1

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Lets say:

x' + x = f(t)

with an initial condition of x(t=0,t')=0;

Step 1 would be to re-write this as:

G(t,t') + G(t,t') = [itex]\delta[/itex](t-t')

then do you multiply by f(t')[itex]\oint[/itex]dt' ?

which I would believe would give me:

s G(s) + G(s) = e^-st

and G(s) = [itex]\frac{1}{s+1}[/itex] e^-st'

then giving me my G(t,t') = e^-(t-t') * U(t-t') ?

Not sure if that is the expected Green's function or if I screwed up somewhere.

Also, if f(t) = U(t-1), what would be the system's response?

* U fxn is a Heaviside step function