Consider the following one-parameter families of first-order differential equations defined on the reals: $$ \dot x = \mu - x - e^{-x} $$ $$ \dot x = x(\mu + e^x) $$ $$ \dot x = x - \frac{\mu x}{1+x^2}$$ Determine the critical points and the bifurcation values, plot vector fields on the line, and draw a bifurcation diagram in each case.
I'm having trouble getting started with this problem because in class, we always worked with a system of equations - $\frac{dx}{dt}$ and $\frac{dy}{dt}$. If anyone could give me a technique to go about finding the bifurcation values, etc. - that would work with all three of these equations - that would be really helpful.