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For example, we have a system described as :

(D[tex]^{2}[/tex] + 4D + 3)y(t) = (D+5)f(t).

I computed system impulse response which is :

h(t) = 2e[tex]^{-t}[/tex] - e[tex]^{-3t}[/tex]

Now if say f(t) = e[tex]^{t}[/tex]

f(t) (convolved) h(t) does not equal the particular solution of D.E. (Particular solution is zero-state) .

Why ??