Chapter 10.7, Problem 14E

The differential equation $y\text{'}=0.5(1-y)(4-y)$ has five types of solutions labelled A-E. For each of the following initial values, graph the solution of the differential equation and identify the types of solution, Use a small value of $h$, let $t$ range from $0$ to $4$ and let $y$ range from $-1$ to $5$. Use the technique of Section10.6 to verify your Answer.

$y(0)=0.9$

$y(0)=1.1$

$y(0)=3$

$y(0)=4$

$y(0)=5$

Constant solution

Decreasing, has an inflection point, and asymptotic to the line $y=1$.

Increasing, concave down, and as asymptotic to the line $y=1$.

Concave up and increasing indefinitely.

Decreasing, concave up, and asymptotic to the line $y=1$.