Find a function 0f nH al =0 y Co) = 7 y (o) =/

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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Question
6
Find
al
9 fuuctio n 0f
8y"ry't&y=
y Co) = 7
y(a)= ?
y co) =/
y"(0)=70
6.
ylu):
Transcribed Image Text:Find al 9 fuuctio n 0f 8y"ry't&y= y Co) = 7 y(a)= ? y co) =/ y"(0)=70 6. ylu):
Expert Solution
Step 1

The differential equation is given as

y'''-8y''-y'+8y=0

The corresponding auxiliary equation is

m3-8m2-m+8=0m2(m-8)-1(m-8)=0(m2-1)(m-8)=0(m+1)(m-1)(m-8)=0m=-1,1,8

Hence the complementary function is

y=C1ex+C2e-x+C3e8x                              (1)

Then

y'(x)=C1ex-C2e-x+8C3e8x                       (2)

and

y''(x)=C1ex+C2e-x+64e8x                         (3)

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