Determine the longest interval in which the given initialvalue problemis certainto have a unique twicedifferentiable solution. Do not attempt to find the solutionty'' + 3y = t, y (1) = 1, y' (1) = 9

t_o = 3, so solution exists on (0,4).

Step-by-step explanation:

Use Theorem

Divide equation with t (t - 4).

y''+[3 / (t-4) ]*y' + [4/t (t-4) ]*y=2/t (t-4)

p (t) = 3/t-4-> continuous on (-∞, 4) and (4,∞)

q (t) = 4/t (t-4) - > continuous on (-∞,0), (0,4) and (4, ∞)

g (t) = 2/t (t-4) - > continuous on (-∞, 0), (0,4) and (4,∞)

t_o = 3, so solution exists on (0,4).