Let o(t) = 0 and use the method of successive approximations to solve the initial value...

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Let o(t) = 0 and use the method of successive approximations to solve the initial value problem y' = t²y - 5t, y(0) = 0. a) Determine (t) for an arbitrary value of n. on(t) = b) Use a graphing utility to plot ₁(t) for n = 1,...,4. Observe whether the iterates appear to be converging. The iterates c) Show that the sequence {(t)} converges. Using Pn(t) = ₁(t) + [₂(t) — ₁(t)] + [3(t) — ₂(t)] + ... + [n(t)- n-1(t)] and the fact that $(0)| Ok(t)| k-1(t)| | Pk+1(t)- ok(t) - the convergence of {n(t)} follows for any t by the Ratio test. = Let o(t) = 0 and use the method of successive approximations to solve the initial value problem y' = t²y - 5t, y(0) = 0. a) Determine (t) for an arbitrary value of n. on(t) = b) Use a graphing utility to plot ₁(t) for n = 1,...,4. Observe whether the iterates appear to be converging. The iterates c) Show that the sequence {(t)} converges. Using Pn(t) = ₁(t) + [₂(t) — ₁(t)] + [3(t) — ₂(t)] + ... + [n(t)- n-1(t)] and the fact that $(0)| Ok(t)| k-1(t)| | Pk+1(t)- ok(t) - the convergence of {n(t)} follows for any t by the Ratio test. =