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Verify that the signals in Exercises 1 and 2 are solutions of the accompanying difference equation..$$3^{k},(-3)^{k} ; y_{k+2}-9 y_{k}=0$$

$( - 3 ) ^ { k }$ is a solution of the difference equation.

Calculus 3

Chapter 4

Vector Spaces

Section 8

Applications to Difference Equations

Vectors

Johns Hopkins University

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

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Verify that the signals in…

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so we need to prove that this to signal stay to the game. I missed a to the K soul of this defense situation. Why scared? Plus to minus nine with Black by Y. K. The only thing we need to do is to just substitute. It's one off the signals vacation and very far you take assume this indeed such fight. So we start with three to the K and week of city to take a plus two minus nine with played by three. So the k they close say so The cave will replied by very squared with his nine minus nine multiplied by cities to the K. And it's now what abuse? That this difference equals zero things. Three squared equals no, and we are done in this part. Now we proceed to the other case to the signal miners A to the k A. Substitute it. So the vacation and we have three to the K plus toe minus nine. What's the blood? By minus three toe take a and these equals minus three to take a multiplied by minus. City squared, which is nine as it is three squared and weeks obstruct nine would declined by minus said it was a K and in the same month at us. Before we have that my mystery squared equals nine. So this difference equals zero. Thus, minus three to the case satisfies this different security zone, and we're done.

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