In Problems 1 through 10, find a power series solution of the given differential equation. Determine the
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In Problems 1 through 10, find a power series solution of the given differential equation. Determine the radius of convergence of the resulting series, and use the series in Eqs. (5) through (12) to identify the series solution in terms of familiar elementary functions.
y' = y
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and || COS X = sin.x = coshx = M8 M8 M8 |- || - x Σ n=0 Σ n=0 ∞0 sinh x = Σ n=0 H=0 n! = 1 + x + (-1)" x²n (2n)! (-1)"x²n+1 (2n + 1)! xan (2n)! x2n+1 (2n + 1)! = 1 00 (−1)n+1x" In(1 + x) = Σ n=1 n = 1+ (1 + x) = 1 + ax + 2! = * =X- 2! 2! 4! =-- α(α – 1)x2 2! 3! x 3 3! x2 4! + + _x" = 1 + x + x2 + x +…; n=0 για 5! 3 3 α(α − 1)(α – 2)x3 3! +... (5) (6) (7) (8) (9) (10) (11) (12)
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Related Book For
Differential Equations And Linear Algebra
ISBN: 9780134497181
4th Edition
Authors: C. Edwards, David Penney, David Calvis
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