Use Taylor's method of order two to approximate the solution for the following IVP. Give the...
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Use Taylor's method of order two to approximate the solution for the following IVP. Give the values of the function at each mesh point and attach your code to the solution. y' = 22ty, 0≤t≤ 1, y(0) = 1, with h = 0.1. Given the secondorder IVP: y" = p(t)y' + q(t)y + r(t), a ≤ t ≤ b, y(a) = a₁, y'(a) = α₂ Let p(t), g(t), r(t) be continuous functions on [a, b]. Convert to a system of firstorder equations and then use a theorem from class to prove a unique solution exists. Determine if the following multistep method for approximating the solution to the IVP y' = f(t, y), a ≤ t≤ b, y(a) = a is stable: Wi+1 = 2w₁1  W₁ + 1/2 [5f (ti, wi) + f(ti1, Wi1)]
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