2. Now consider the modified IVP y(0) = 0 a) Find the sequence of Picard iterate

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2. Now consider the modified IVP y(0) = 0 a) Find the sequence of Picard iterates and the limit function (t) = lin (t). b) Does the first iterate (t) satisfy the ODE for any values of t? Is 1(t)s solution on any interval around t = 0? c) Verify that the limit function (t) satisfies the differential equation directly by using term-by-term differcntiation on the scrics. d) Use the Taylor series of er to express (t) in closed-form. e) Verify your solution by using the method of integrating factors.

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