If y(t) + ∞y(τ) x(t – τ )dτ = S(t) + x(t) then y(t)

y(t) +		^∞	y(τ) x(t – τ )dτ = δ(t) + x(t) …(A)
		0

L.H.S. = y(t) +		^∞	y(τ) x(t – τ )dτ
		0

= y(t) + y(t) * x(t)
If we compare the equation with R.H.S part of equation (A), we conclude that
y(t) = δ(t) {∵ x(t) * δ(t) = x(0)}

If y(t) +		^∞	y(τ) x(t – τ )dτ = S(t) + x(t) then y(t) is—
		₀