Question
Asked Jul 1, 2019
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Find the first five nonzero terms in the solution to the initial value problem:

y"-2xy'+8y=0, y(0)=3, y'(0)=0

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Expert Answer

Step 1

n-2
n
2
8
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n-2 n 2 8

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Step 2

Comparing constant terms on each sides,

C22 8 0
C2 2-8c
( y(0)3=c)
c2=-4(3)
c212
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C22 8 0 C2 2-8c ( y(0)3=c) c2=-4(3) c212

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Step 3

Comparing coefficient of x ...

сз -3-2-2с, + 8c, %3D0
бс, + бс, %3D0
(:У(0)-0-с)
Сз %3-0
С, 30
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сз -3-2-2с, + 8c, %3D0 бс, + бс, %3D0 (:У(0)-0-с) Сз %3-0 С, 30

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