Question 1

Find the orthogonal trajectories of the family of curves.

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Question 2

Solve the initial-value problem.

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Question 3

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

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Question 4

Select a direction field for the differential equation  from a set of direction fields labeled I-IV.

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Question 5

An object with mass  is dropped from rest and we assume that the air resistance is proportional to the speed of the object.If  is the distance dropped after t seconds, then the speed is  and the acceleration is  .If g is the acceleration due to gravity, then the downward force on the object is  where  is a positive constant, and Newton's Second Law gives  Find the limiting velocity.

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Question 6

Solve the initial-value problem.

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Question 7

Let c be a positive number.A differential equation of the form  where  is a positive constant, is called  because the exponent in the expression  is larger than the exponent 1for natural growth.An especially prolific breed of rabbits has the growth term  If  such rabbits breed initially and the warren has  rabbits after months, then when is doomsday?

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Question 8

A certain small country has $20 billion in paper currency in circulation, and each day $70 million comes into the country's banks.The government decides to introduce new currency by having the banks replace old bills with new ones whenever old currency comes into the banks.Let  denote the amount of new currency in circulation at time t with  Formulate and solve a mathematical model in the form of an initial-value problem that represents the "flow" of the new currency into circulation (in billions per day).

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Question 9

Let  What are the equilibrium solutions?

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Question 10

One model for the spread of an epidemic is that the rate of spread is jointly proportional to the number of infected people and the number of uninfected people.In an isolated town of  inhabitants,  people have a disease at the beginning of the week and  have it at the end of the week.How long does it take for  of the population to be infected?

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Question 11

Suppose that a population grows according to a logistic model with carrying capacity  and  per year.Write the logistic differential equation for these data.

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Question 12

Solve the initial-value problem.

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Question 13

Solve the differential equation.

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Question 14

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

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Question 15

Biologists stocked a lake with  fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be  The number of fish tripled in the first year.Assuming that the size of the fish population satisfies the logistic equation, find an expression for the size of the population after t years.

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Question 16

Kirchhoff's Law gives us the derivative equation  If  use Euler's method with step size 0.1 to estimate  after 0.3 second.

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Question 17

A function  satisfies the differential equation  What are the constant solutions of the equation?

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Question 18

Find the solution of the initial-value problem and use it to find the population when

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Question 19

Solve the differential equation.

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Question 20

A sum of  is invested at  interest.If  is the amount of the investment at time  or the case of continuous compounding, write a differential equation and an initial condition satisfied by

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Quiz 9: Differential Equations

Find the orthogonal trajectories of the family of curves.

Solve the initial-value problem.

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

Select a direction field for the differential equation from a set of direction fields labeled I-IV.

Solve the initial-value problem.

Let What are the equilibrium solutions?

Suppose that a population grows according to a logistic model with carrying capacity and per year.Write the logistic differential equation for these data.

Solve the initial-value problem.

Solve the differential equation.

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

Kirchhoff's Law gives us the derivative equation If use Euler's method with step size 0.1 to estimate after 0.3 second.

A function satisfies the differential equation What are the constant solutions of the equation?

Find the solution of the initial-value problem and use it to find the population when

Solve the differential equation.

A sum of is invested at interest.If is the amount of the investment at time or the case of continuous compounding, write a differential equation and an initial condition satisfied by