OK, this is a weak question, but I'm a bit rusty on differential equations, so here it is:
I need to find the general solution of x'=ax+3 and then find the equilibrium points as well as which points are equilibria sinks and sources (a is a parameter).
I found the general solution of x(t). It was: $x(t)=Ce^{at}-\frac{3}{a}$
Now, from the one or two lines in the text about equilibrium points, I'm seeing that that will be a "value" that makes x(t) = 0. Though, the way it's worded in the text makes it seem like a choice of "a" or "C" will be what makes an equilibrium solution.
This is where I'm confused. Do I solve the general solution for t by setting x = 0? Do I solve the original equation finding setting x' to 0 and finding x (this is what I saw on some website).
I'm just not sure what I'm supposed to do to find the equilibrium points, and then how to decide which are sinks and which are sources.