3 the equation can be re written as y y 12 e2x

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Unformatted text preview: icular solutions of the form k1 e2x and k2 , we find k1 = 1/3 and k2 = 1, respectively. Answer: 1 y = C1 ex + C2 e−x + e2x + 1. 3 (∗) The equation can be re-written as (y ′′ − y + 1)2 = e2x , or y ′′ − y = ±ex − 1. Answer: 1 y = C1 ex + C2 e−x ± xex + 1. 2 an+1 = |x| < 1, and diverges if |x| > 1. At |x| = 1, the an ∞ ∞ ∞ ∞ 2n + 1 1 2n + 1 1 + 2−n n series > diverges, and the series (−1) = (−1)n 2n n n 2n n n n=1 n=1 n=1 n=1 ∞ 1n x+ converges. Note that the original series can be split in two: S (x) = n n=1 ∞ 1 xn where the fir...
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This document was uploaded on 03/02/2014 for the course PHYSICS 3513 at Oklahoma State.

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