Solving Non-homogeneous ODEs using Power Series

teddy_boo
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Homework Statement



y"+3y'+2y= sin x

y(0)=0
y'(0)=1

Evaluate y(0.1)

Homework Equations



Power Series Equation

The Attempt at a Solution

 
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I see nothing under "3. The Attempt at a Solution "!

An oversight, no doubt?
 
Oh, I'm so sorry, let me edit the post for a while
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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