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Problem XII.3 п (a) Suppose the power series Anxn converges to a function y=y(x) such that n=0 - = = = 2 > y" -y'+y = 0,
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Problem XII.3 п (a) Suppose the power series Anxn converges to a function y=y(x) such that n=0 - = = = 2 > y" -y'+y = 0,
Problem XII.3 п (a) Suppose the power series Anxn converges to a function y=y(x) such that n=0 - = = = 2 > y" -y'+y = 0, y(0) = 1, y'(0) = 0. Find a formula that expresses an+2 in terms of an+1 and an and determine 20, 21, 22, a3. (b) Solve the initial-value problem in (a) exactly (find a simple formula for y=y(x)). (c) Use your answer in (b), Taylor series, and multiplication of power series to recover the values of ao, Q1, Q2, A3 you found in (a). >
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