Write a 2nd order DE given two particular solutions

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The discussion centers on deriving a second-order linear differential equation given two particular solutions: y1 = -3e^(2t) and y2 = e^(2t) + 2te^(2t). The characteristic equation is identified as (r - 2)^2 = 0, leading to the differential equation y'' - 4y' + 4y = 0. This confirms that the problem involves a repeated root scenario, which simplifies the solution process. Participants affirm that the problem is straightforward and encourages confidence in solving similar equations.

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PNGeng
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The question is:

Find a second order linear equation which has y1=-3e^(2t) and y2=e^(2t)+2te^(2t) as two of its particular solutions.

Attempt at a solution:

Since it's a repeated root problem, we know r=2, therefore the characteristic equation must look like (r-2)^2=0

r^2-4r+4=0 ----------------------- > y''-4y'+4y=0
Is this problem really that easy? I have a feeling I'm misinterpreting the question cause this is way too trivial.
 
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Yes, it is that easy. Enjoy it. :smile:
 

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