Now solve the ordinary differential equation (ODE) boundary value problem: v"(y) – X²v(y) = 8(y – &y), 0< §, < 2 v(0) = v(2) = 0, where A is a constant and ' denotes differentiation with respect to y. Simplify your answer as far as possible. Hint: It will be helpful to write down the solution of the ODE in terms of hyperbolic functions.

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