The first two problems on this quiz are simply vocabulary.
This top equation is a differential equation, as it has both functions and their derivatives mixed in
This equation has no derivatives in it and is not a differential equation
Differential equations are used to model flows
The second equation is a difference equation
Difference equations are used to describe or model maps
Question 3 asks us to characterize each of these four fixed points as stable, unstable, or chaotic
As it makes no sense to have a chaotic fixed point, we can eliminate this choice from all of the questions
To analyze whether these fixed points are stable or unstable, we need to know whether a small perturbation near the fixed point grows or shrinks
For this first fixed point, notice that a small perturbation quickly shrinks down and the pendulum returns to the original fixed point
So this fixed point is stable. That is the answer to 3a
For this fixed point in figure 1b, notice that the small perturbation caused by my finger rapidly grows
That means this fixed point is unstable. That is the answer to 3b
Notice for c and d, I have to hold them in position
That is, they are so unstable, I cant even get them to balance at this point
That should give you a hint as to the answer for these problems
But to make it very clear, watch small perturbations of both c and d
As you can see, both c and d are also unstable fixed points. That is the answer to 3c and 3d