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Differential equation

The question is to find the particular integral of the DE
y2y+y=exx2+1. \displaystyle y''-2y'+y=\frac{e^x}{x^2+1}.
It seems to be quite tough and not just straight forward. What trial function should I try?
Original post by Ano123
The question is to find the particular integral of the DE
y2y+y=exx2+1. \displaystyle y''-2y'+y=\frac{e^x}{x^2+1}.
It seems to be quite tough and not just straight forward. What trial function should I try?


Wolfram suggests something with ln(x^2+1) and arctan x. See http://m.wolframalpha.com/input/?i=solve+y%27%27-2y%27%2By%3D%28e%5Ex%29%2F%28x%5E2%2B1%29&x=0&y=0
Reply 2
Use variation of parameters to find the particular integral.

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