# Worksheet: Separable Differential Equations

Q1:

Solve the differential equation .

• A
• B
• C
• D
• E

Q2:

The logistic population model assumes an upper limit , beyond which growth cannot occur. The population has a rate of change that satisfies for some positive constant . A suitable function involves a second parameter , determined by how rapid the initial growth is. Without integrating, which of the following could be ?

• A
• B
• C
• D
• E

Q3:

Solve the differential equation .

• A or
• B or
• C or
• D or
• E or

Q4:

Suppose a populationβs growth is governed by the logistic equation , where . Write the formula for .

• A
• B
• C
• D
• E

Q5:

Suppose a populationβs growth is governed by the logistic equation , where . Write the formula for .

• A
• B
• C
• D
• E

Q6:

Solve the following differential equation by separating it:

• A
• B
• C
• D

Q7:

Unlike exponential growth, where a population grows without bound, the logistic model assumes an upper limit , beyond which growth cannot occur. The population has a rate of change that satisfies for some positive constant . Given a population with , at what population is the growth zero?

• A
• B0
• CIt cannot be determined.
• D
• Enever

Q8:

Find a 1-parameter family of solutions for the following differential equation:

• A
• B
• CThere is no solution.
• D

Q9:

Find the solution of the differential equation given that .

• A
• B
• C
• D

Q10:

Find the implicit solution to the following differential equation:

• A
• B
• C
• D

Q11:

Which of the following is a solution of defined for all ?

• A
• B
• C
• D

Q12:

Find a relation between and given that .

• A
• B
• C
• D
• E

Q13:

Find the solution for the following differential equation for :

• A
• B
• C
• D

Q14:

Solve the differential equation .

• A
• B
• C
• D

Q15:

Suppose a population grows according to a logistic model with an initial population of 1β000 and a carrying capacity of 10β000. If the population grows to 2β500 after one year, what will the population be after another three years?

Q16:

Find the solution of the differential equation that satisfies the initial condition .

• A
• B
• C
• D
• E