For the initial value problem
y″ = y′ + y, y(0) = 0, y(1) = 1
derive the power series solution
where is the sequence 0, 1, 1, 2, 3, 5, 8, 13,... of Fibonacci numbers defined by F0 = 0, F1 = 1, Fn = Fn-2 + Fn-1 for n > 1.
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