Question 7.3.6: Finding Equilibrium Solutions Find all equilibrium solutions...

An equilibrium solution is a constant solution that reduces the equation to
y′(t) = 0. For part (a), this gives us

0=y^{\prime}(t)=k[y(t)-70] \quad \text { or } \quad 0=y(t)-70.

The only equilibrium solution is then y = 70. For part (b), we want

0=2 y(t)[4-y(t)] \quad \text { or } \quad 0=y(t)[4-y(t)].

So, in this case, there are two equilibrium solutions: y = 0 and y = 4.