Question
Asked Aug 1, 2019
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Differential equations:

Using the power series method, find the particular solution to the initial value problem:

y"+x2y'+xy=0,   y(0)=3, y'(0)=1

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Expert Answer

Step 1

Consider the given initial value problem:

y"+x2y4xy=0, y(0)=3, y'(0)=1
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y"+x2y4xy=0, y(0)=3, y'(0)=1

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Step 2

Suppose the power series solution is:

y= 2 a,,rn
n-0
then
y'= na,r"-
n=1
y"= n(n-1)a/,*"-2
n-2
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y= 2 a,,rn n-0 then y'= na,r"- n=1 y"= n(n-1)a/,*"-2 n-2

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Step 3

Now, put these values in...

n(n-1)apx'
n=2
_
n=1
n=0
n(n-1)a
N=2
1
n=1
n=0
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n(n-1)apx' n=2 _ n=1 n=0 n(n-1)a N=2 1 n=1 n=0

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