Chapter 10.7, Problem 13E

(a)

To determine

To graph: The solution of the differential equation $y\text{'}=0.5(1-y)(4-y)$ with initial condition $y(0)=-1$, where $t$ ranges from $0\text{to}\text{4}$ and $y$ ranges from $-1\text{to}\text{5}$. And, identify the type of solution from the following types:

A. Constant solution

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

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

D. Concave up and increasing definitely.

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

(b)

To determine

To graph: The solution of the differential equation $y\text{'}=0.5(1-y)(4-y)$ with initial condition $y(0)=1$ where $t$ range from $0\text{to}\text{4}$ and $y$ ranges from $-1\text{to}\text{5}$. And, identify the type of solution from the following types:

A. Constant solution

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

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

D. Concave up and increasing definitely.

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

(c)

To determine

To graph: The solution of the differential equation $y\text{'}=0.5(1-y)(4-y)$ with the initial condition $y(0)=2$, where $t$ ranges from $0\text{to}\text{4}$ and $y$ ranges from $-1\text{to}\text{5}$. And, identify the type of solution from the following types:

A. Constant solution

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

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

D. Concave up and increasing definitely.

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

(d)

To determine

To graph: The solution of the differential equation $y\text{'}=0.5(1-y)(4-y)$ with initial condition $y(0)=3.9$ where $t$ range from $0\text{to}\text{4}$ and $y$ ranges from $-1\text{to}\text{5}$. And, identify the type of solution from the following types:

A. Constant solution

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

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

D. Concave up and increasing definitely.

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

(e)

To determine

To graph: The solution of the differential equation $y\text{'}=0.5(1-y)(4-y)$ with initial condition $y(0)=4.1$ where $t$ range from $0\text{to}\text{4}$ and $y$ ranges from $-1\text{to}\text{5}$. And, identify the type of solution from the following types:

A. Constant solution

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

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

D. Concave up and increasing definitely.

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