Write down a differential equation of the form dy/dt = ay + b whose solutions have the required behavior as t → ∞. all other solutions diverge from y = 2.

We have that the differential equation of the form dy/dt = ay + b whose solutions have the required behavior as t → ∞. all other solutions diverge from y = 2 is

From the Question we are told that

Generally,

Where

Therefore

Substituting

Then all other solutions diverge from

Therefore

For more information on this visit

link

The ODE has an equilibrium point at

We want to be an unstable equilibrium solution - in other words, we want all solutions with initial condition for near 2 to diverge from - so .

Divergence from would require that for , any solution is increasing, and for , and solution is decreasing. In order for that to happen, we need

if , and

if .

Now we just pick to satisfy these conditions. An easy choice is , which forces , so that one possible ODE would be

I've attached a plot of the slope field to demonstrate the behavior of the solutions.

the answer is c.

for continuous functions, they continue in the same pattern and you have to find that pattern kinda like slope