Word Count : 419

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We are tasked with showing that the function \[ u_{x} = c_1 e^{ax} + c_2 e^{-ax} \] is a solution of the difference equation: \[ u_{x + 1} - 2u_{x} \cosh a + u_{x - 1} = 0 \] ### Step 1: Compute \( u_{x+1} \) and \( u_{x-1} \) Given the general form of the function, we compute the expressions for \( u_{x+1} \) and \( u_{x-1} \). __________ ___ _________ __________ ___.
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