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12 June, 16:34

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

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  1. 12 June, 16:56
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    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).
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