(a) Find the general solution to the following differential equation. Express your answer in terms of Bessel functions of the first and second kinds. Do not write any series expansions of these Bessel functions. Please explain how you arrived at your answer. x²y" + xy' + (2x² - 5)y = 0 (b) Solve the heat flow problem. Please start with the formula for u(x, t); Do not show separation of variables. Simplify your answer as much as possible. ди Ət = J²u 2 მე2 u(0,t) = u(5,t) = 0 x, 0 < x <1 u(x, 0): = 1, 1 ≤ x < 4 0, 4≤x≤5

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