Let (t) be the solution of the initial-value problem d2 y
Chapter , Problem 9(choose chapter or problem)
Let (t) be the solution of the initial-value problem d2 y dt2 + p dy dt + qy = 0(t), y(0) = y (0) = 0. Let a and b be constants and let f (t) be an arbitrary function. (a) Find an expression for the Laplace transform of the solution of the initial-value problem d2 y dt2 + p dy dt + qy = 0, y(0) = a, y (0) = 0 in terms of a, p, q, and L[ ]. (b) Find an expression for the Laplace transform of the solution of the initial-value problem d2 y dt2 + p dy dt + qy = 0, y(0) = 0, y (0) = b in terms of b, p, q, and L[ ]. (c) Find an expression for the Laplace transform of the solution of the initial-value problem d2 y dt2 + p dy dt + qy = f (t), y(0) = a, y (0) = b in terms of a, b, p, q, L[ f ], and L[ ].
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