Find the general solution of the given differential equation:
$$ (x^2-4)\left(\frac{dy}{dx}\right) +4y = (x+2)^2 $$
I found the general solution of the D.E and I got the following correct solution:
$$ y = (x+C)\left(\frac{x+2}{x-2}\right) $$
I know that this is the correct solution and the next part of the question says to determine whether there are any transient terms in the general solution. (Enter the transient terms as a comma-separated list; if there are none, enter NONE.)
The definition of a transient term from my understanding is a term that approaches zero as x goes to infinity.
Ive tried many answers and do not know how to find the transient terms. I thought there were none in this solution.
Can anyone guide me in understanding the problem?
Thanks.
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