$$x' = x^2 + \mu$$
Draw the graph for $\mu = 1$, $\mu = 0$,and $\mu = −1$.
I can draw the graph for this equation, which turns out to be like this:
But how do I find the equilibria of this particular differential equation? Or maybe how can I find equilibria of any equation?
One kind of equilibrium is about the motion of some particle in a potential field $$ \DeclareMathOperator{grad}{grad} m \ddot{x} = - \grad V(x) $$ The shape of the potential field $V(x)$ may have points where the particle would rest. Depending on the neighbourhood it could be a stable equilibrium or not. (Think of a marble in a concave spot vs a marble on a convex top).
Maybe your task goes into that direction.
For this you need to explain what is meant by the $x'$ term. Is it the derivative regarding to some variable?
Your graph shows the points $(x, x')$ where $x' = x^2 + \mu$.