Non-homogeneous series equation

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The discussion focuses on solving the non-homogeneous differential equation y'' - 4xy' + 3y = e^(-x) with initial conditions y(0) = 1 and y'(0) = 1. Participants emphasize the necessity of using power series methods to derive the first four terms of the solution. Additionally, they highlight the importance of establishing a recurrence relation to facilitate the computation of subsequent terms in the series expansion.

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hbomb
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could someone help me start of the series for this equation

y"-4xy'+3y=e^(-x)
y(0)=1
y'(0)=1

I'm not sure what to do since this is not a homogeneous equation.
 
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I'm staring at that, wondering why you don't just substitute 0 for x, and substitute 1 for y, and 1 for y'? But, I looked at your equations before I even read your sentence about finding a series.
 
I'm required to find the first four values of this equation. And then I'm suppose to find a recurrence relation of this equation.
 

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