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1. y" + y = 0

1. y" + y = 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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12:55 о all atl & 16 Power Series Solution Usin... Activity 3 1. у" + у30 Power Series >. anx" = ao + a1x + azx² + a3x³ + anx" n=0 y = a, + a1x + azx² + azx³ + a4x* y' = a1 + 2a2x + 3azx² + 4a4x³ у" %3D 2а, + 6азх + 12а,x2 y" = 6az + 24a4x yiv = 4.3.2a4 ex1.y' - у %3D 0 (а, + 2а2x + Зазx2 + 4а,x3) - (аo +a,x +azx2 + азх3 + а,х4) a1 - ao = 0, a = ao a, 2a2 – a1 = 0, a = ao 2 2! ao a2 3az - az = 0, az = ao %D 3! ao az 4a4 – az = 0, a4 = do %3D 4! y = f(x) = ao + a,x + a2x² + azx³ aox3 + 3! a,x? aox* y = ao + aox + 2! 4! x2 x3 x* 4! doe* 1 of 2 y = ao 1+x 2!
Transcribed Image Text:12:55 о all atl & 16 Power Series Solution Usin... Activity 3 1. у" + у30 Power Series >. anx" = ao + a1x + azx² + a3x³ + anx" n=0 y = a, + a1x + azx² + azx³ + a4x* y' = a1 + 2a2x + 3azx² + 4a4x³ у" %3D 2а, + 6азх + 12а,x2 y" = 6az + 24a4x yiv = 4.3.2a4 ex1.y' - у %3D 0 (а, + 2а2x + Зазx2 + 4а,x3) - (аo +a,x +azx2 + азх3 + а,х4) a1 - ao = 0, a = ao a, 2a2 – a1 = 0, a = ao 2 2! ao a2 3az - az = 0, az = ao %D 3! ao az 4a4 – az = 0, a4 = do %3D 4! y = f(x) = ao + a,x + a2x² + azx³ aox3 + 3! a,x? aox* y = ao + aox + 2! 4! x2 x3 x* 4! doe* 1 of 2 y = ao 1+x 2!
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