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Homework Statement
Find the Impulse response of this system
3y[n]+4y[n-1]+y[n-2] = x[n] + x[n-1]
Homework Equations
Eigenvalues = -1/3 and -1
hc[n] = k1[-1/3]n+k2[-1]n
3h[n] +4h[n-1] +h[n-2] = δ[n] + δ[n+1]
The Attempt at a Solution
I know that normally we would plug in hc[n] for two values of n into our given equation giving us a system of two equations for k1 and k2
However, since the answer for this inolves δ[n] + δ[n+1] I feel like there is a different approach.
I'm not really sure where to go after finding hc[n]