For each of the following differential equation problems, state how many arbitrary constants you would expect to find in the most general solution satisfying the problem. Find the solution and check whether your expectation is confirmed.

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(a) (b) (c) (d) (e) (f) dx dt dx dt dx dt d.x dt dx dr dx dt = 4t, x(0) = 2 = sin 2t, x) = 2, x() = 2 + 2t = 0, x(1) = 1 = 2e-2, x(0) = a - 2 sin 2t = 0