Find the Differential Equation

The questions below are due on Thursday February 20, 2025; 02:00:00 PM.
 
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Let \delta[n] represent the unit-sample signal:

\delta[n] = \cases{1&if $n=0$\cr0&otherwise\cr}
Find constants c_1, c_2, and c_3 so that the solution to the difference equation

c_1y[n{-}1]+c_2y[n]+c_3y[n{+}1] = \delta[n]

is equal to the signal y[n] shown below.


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