To solve the algebraic equation y – y? + € = 0, we set /2, | y = e2y1 + eY2 + e/2y3+... , then to find the O(e/2), we solve Y = 2yı y3 = 3yfy2 – y 3 Y1 Y2 = 4y? Y2 = y? 3 Y1Y2 = 2y} 2y2 = yỉ vỉ = 1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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To solve the algebraic equation
y – y? + € = 0, we set
e/2y1 + ey2 + e/2y3+... ,, then to
find the O(e/2), we solve
3/2,
= E
2y1 y3 = 3yy2 – y?
Y1Y2 = 4y
4y
Y2 = y?
Y1 Y2 = 2y?
%3D
2y2 = yỉ
y = 1
Transcribed Image Text:To solve the algebraic equation y – y? + € = 0, we set e/2y1 + ey2 + e/2y3+... ,, then to find the O(e/2), we solve 3/2, = E 2y1 y3 = 3yy2 – y? Y1Y2 = 4y 4y Y2 = y? Y1 Y2 = 2y? %3D 2y2 = yỉ y = 1
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