IGNOU MTE 10 2018 - Show that ux = c1eax + c2e-ax is a solution of the difference equation

Question

Show that ux = c₁e^ax + c₂e^-ax is a solution of the difference equation
u_x+1 - 2u_x cosh $\alpha_{x-1} =0$ .

14 Feb 2018

Answer :

Word Count : 308

Let's solve the given problem step by step. We are tasked to show that the function $ u_x = c_1 e^{ax} + c_2 e^{-ax} $ is a solution to the difference equation: \[ u_{x+1} - 2u_x \cosh(\alpha_{x-1}) = 0 \] ### Step 1: Write out the expressions for $ u_{x+1} $ and $ u_x $. We are given: \[ u_x = c_1

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