Differential equation asymptotes
Hi guys, I just have a very broad and general question.
Today in math class I was asked to solve the horizontal asymptote of a differential equation, and this had me stumped.
Later on, the teacher gave me the following two examples:
The solution to the first equation for a horizontal asymptote is DNE
The solution to the second is 2
Now, I'm just wondering... How would one know that this is true without solving for the original equation? I mean, this doesn't seem intuitive at all to me. Why is it that when X is what makes the differential equation 0 there is no asymptote and when Y makes the equation 0 there is?
Thanks for all the help.