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I was wondering what substitution to try when finding a particular solution for a recurrence equation with a linear combination of impulses on the right side of the equation. I think an example will clarify this.

Given the recurrence equation

[tex]y[k+2]-4y[k]=\delta [k] + 2\delta [k+1][/tex]

with [tex]\delta [k][/tex] being the discrete impulse, i.e [tex]\delta [k] = 1[/tex] for [tex]k=0[/tex] and [tex]\delta [k] = 0[/tex] for [tex]k\neq 0[/tex].

First you must find a solution for the homogeneous equation. I have no problems with that. But I don't know what substitution to use for finding the particular solution? Can someone help me with that?

Thanks,

Yoran

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# Substitution for impulse in recurrence equation

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