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2. Find the first three nonzero terms in a power series expansion about to = 0...


2. Find the first three nonzero terms in a power series expansion about to = 0 of the solution of the initial value problem y
2. Find the first three nonzero terms in a power series expansion about to = 0 of the solution of the initial value problem y" - xy + 2y = 0, y(0) = 0,7'0) = 1. Hint: Compute up to 25.
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# Lel y -xy tay=0 lel y anton y = E nan xny y = xn-2 E n(n-1) an 1-2 ܥ IMP E non-isan Xn-2 + n=2 San X=- - nanan + o n(n-29 +290)*+ (69z+2a,-a,)x+ § {n+2)(n+1) Ch+2 n-2 -nantzan] X=0 ₂ +0=0 au = -a o Gazta, az = an ( (n+2)(n+1) antit Entl) an aS (... - * - * - * = و 6 thus first three non-zero team! jespectively, دیا۔ - ا =

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2. Find the first three nonzero terms in a power series expansion about to = 0...
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