In each of Problems 1 through 4, determine (without solving the problem) an interval in which the solution of the given initial value problem is certain to exist.

1. (t - 3)y' + (ln t)y = 2t, y(1)=2

2. y' + (tan t) y = sin t, y(pi) = 0

3. (4 - t^2)y' + 2ty = 3t^2, y(-3) = 1

4. (ln t)y' + y = cot t, y(2) = 3