4.1.1 Identify the following as pure-time differential equations or autonomous differential equations. ...
Get solution
4.1.2 Identify the following as pure-time differential equations or autonomous differential equations. ...
Get solution
4.1.3 Identify the following as pure-time differential equations or autonomous differential equations. ...
Get solution
4.1.4 Identify the following as pure-time differential equations or autonomous differential equations. ...
Get solution
4.1.5
Use the graph of the rate of change to sketch a graph of the
function, starting from the given initial condition. Start from x(0) = 1. ...
Get solution
4.1.6
Use the graph of the rate of change to sketch a graph of the
function, starting from the given initial condition. Start from y(0)=−1. ...
Get solution
4.1.7
Use the graph of the rate of change to sketch a graph of the
function, starting from the given initial condition. Start from z(0) = 2. ...
Get solution
4.1.8
Use the graph of the rate of change to sketch a graph of the
function, starting from the given initial condition. Start from w(0) = 1. ...
Get solution
4.1.10 Check
that the following are solutions of the given differential equation.
What was the initial condition (the value of the state variable at t = 0)? ...
Get solution
4.1.10 Check
that the following are solutions of the given differential equation.
What was the initial condition (the value of the state variable at t = 0)? ...
Get solution
4.1.11 Apply Euler’s method to the following differential equations to estimate the solution at t = 1 starting from the given initial condition. First, use one step with Δt = 1, and then use two steps with Δt = 0.5. Compare with the exact result from the earlier problem. ... with initial condition x(0) = 1 (as in Exercise 9).
Get solution
4.1.12 Apply Euler’s method to the following differential equations to estimate the solution at t = 1 starting from the given initial condition. First, use one step with Δt = 1, and then use two steps with Δt = 0.5. Compare with the exact result from the earlier problem. ... initial condition w(0)=3 (as in Exercise 10).
Get solution
4.1.13 For
each of the following descriptions of the volume of a cell, write a
differential equation, find and graph the solution, and say whether the
solution makes sense for all time. A cell starts at a volume of 600 ...and loses volume at a rate of 2 ... per second.
Get solution
4.1.14 For
each of the following descriptions of the volume of a cell, write a
differential equation, find and graph the solution, and say whether the
solution makes sense for all time. A cell starts at a volume of 400 ...and gains volume at a rate of 3 ... per second.
Get solution
4.1.16 The following describe the velocities of different animals. In each case,
a. Draw a graph of the velocity as a function of time.
b. Write a differential equation for the position.
c. Guess the solution of this equation.
d. Draw a graph of the position as a function of time.
e. How long will it take to reach its goal?
Get solution
4.1.16 The following describe the velocities of different animals. In each case,
a. Draw a graph of the velocity as a function of time.
b. Write a differential equation for the position.
c. Guess the solution of this equation.
d. Draw a graph of the position as a function of time.
e. How long will it take to reach its goal?
Get solution
4.1.17 The following describe the velocities of different animals. In each case,
a. Draw a graph of the velocity as a function of time.
b. Write a differential equation for the position.
c. Guess the solution of this equation.
d. Draw a graph of the position as a function of time.
e.
How long will it take to reach its goal? A snail starts crawling
across a sidewalk, trying to reach the other side which is 50 cm away.
The velocity of the snail t minutes after it starts is t cm/min.
Get solution
4.1.18 The following describe the velocities of different animals. In each case,
a. Draw a graph of the velocity as a function of time.
b. Write a differential equation for the position.
c. Guess the solution of this equation.
d. Draw a graph of the position as a function of time.
e. How long will it take to reach its goal? A
cheetah is standing 1 m from the edge of the jungle. It starts
sprinting across the savanna to attack a zebra that is 200 m from the
edge of the jungle. After t seconds, the velocity of the cheetah is ... m/s.
Get solution
4.1.19 Apply Euler’s method with the given value of Δt to
the differential equation. Compare the approximate result with the
exact result from the earlier problem. The cell in Exercise 13. Use a
step size of Δt = 10 to estimate the volume at t = 40.
Get solution
4.1.20 Apply Euler’s method with the given value of Δt to
the differential equation. Compare the approximate result with the
exact result from the earlier problem. The cell in Exercise 14. Use a
step size of Δt = 5 to estimate the volume at t = 30.
Get solution
4.1.21 Apply Euler’s method with the given value of Δt to
the differential equation. Compare the approximate result with the
exact result from the earlier problem. The cell in Exercise 15. Use a
step size of Δt = 10 to estimate the volume at t = 30.
Get solution
4.1.22 Apply Euler’s method with the given value of Δt to
the differential equation. Compare the approximate result with the
exact result from the earlier problem. The cell in Exercise 16. Use a
step size of Δt = 2 to estimate the volume at t = 10.
Get solution
4.1.23 Apply Euler’s method with the given value of Δt to
the differential equation. Compare the approximate result with the
exact result from the earlier problem. The snail in Exercise 17.
Use a step size of Δt = 2 to estimate the position at t = 10.
Get solution
4.1.24 Apply Euler’s method with the given value of Δt to
the differential equation. Compare the approximate result with the
exact result from the earlier problem. The cheetah in Exercise 18. Use a
step size of Δt = 1 to estimate the position at t = 5.
Get solution
4.1.25 Use
the hints to “guess” the solution of the following differential
equations describing the rate of production of some chemical. In each
case, check your solution, and graph the rate of change and the
solution. ... with initial condition P(0) = 0. Start by finding the derivative of ...correct it by multiplying by some constant, and then add an appropriate value to match the initial condition.
Get solution
4.1.26 Use
the hints to “guess” the solution of the following differential
equations describing the rate of production of some chemical. In each
case, check your solution, and graph the rate of change and the
solution. ... with initial condition P(0)= 0. Start by finding the derivative of ...correct it by multiplying by some constant, and then add an appropriate value to match the initial condition.
Get solution
4.1.28 For each of the following measurements, give circumstances under which you could measure the following.
a. The value but not the rate of change.
b. The rate of change but not the value. Mass (rate of change is growth rate).
Get solution
4.1.28 For each of the following measurements, give circumstances under which you could measure the following.
a. The value but not the rate of change.
b. The rate of change but not the value. Mass (rate of change is growth rate).
Get solution
4.1.29 For each of the following measurements, give circumstances under which you could measure the following.
a. The value but not the rate of change.
b.
The rate of change but not the value. Sodium concentration (with rate
of change equal to the rate at which sodium enters and leaves).
Get solution
4.1.30 For each of the following measurements, give circumstances under which you could measure the following.
a. The value but not the rate of change.
b. The rate of change but not the value. Total chemical (with rate of change equal to the chemical production rate).
Get solution
4.1.31 Apply Euler’s method to solve the differential equation ... with the initial condition b(0) = 1.0. Compare with the sum of the results of ... Do
you think there is a sum rule for differential equations? If your
computer has a method for solving differential equations, find the
solution and compare it with your approximate solution from Euler’s
method.
Get solution
