Calculus Volume 2
Calculus Volume 2
17th Edition
ISBN: 9781938168062
Author: Gilbert Strang, Edwin Jed Herman
Publisher: OpenStax
bartleby

Concept explainers

Differential Equations
Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…
bartleby

Videos

Textbook Question
Book Icon
Chapter 4.1, Problem 12E

Verify that the following functions are solutions to the given differential equation.

12. y = e x 2 / 2     solves     x y ' = 1

Expert Solution & Answer
Check Mark
bartleby

Trending nowThis is a popular solution!

See solution
Check out sample textbook solution
Blurred answer
Previous
Chapter 4.1, Problem 11E
Next
Chapter 4.1, Problem 13E

Chapter 4 Solutions

Calculus Volume 2

Ch. 4.1 - Determine the order of the following differential...Ch. 4.1 - Determine the order of the following differential...Ch. 4.1 - Determine the order of the following differential...Ch. 4.1 - Determine the order of the following differential...Ch. 4.1 - Determine the order of the following differential...Ch. 4.1 - Determine the order of the following differential...Ch. 4.1 - Determine the order of the following differential...Ch. 4.1 - Verify that the following functions are solutions...Ch. 4.1 - Verify that the following functions are solutions...Ch. 4.1 - Verify that the following functions are solutions...
Ch. 4.1 - Verify that the following functions are solutions...Ch. 4.1 - Verify that the following functions are solutions...Ch. 4.1 - Verify that the following functions are solutions...Ch. 4.1 - Verify that the following functions are solutions...Ch. 4.1 - Verify that the following functions are solutions...Ch. 4.1 - Verify that the following functions are solutions...Ch. 4.1 - Verify that the following functions are solutions...Ch. 4.1 - Verify the following general solutions and find...Ch. 4.1 - Verify the following general solutions and find...Ch. 4.1 - Verify the following general solutions and find...Ch. 4.1 - Verify the following general solutions and find...Ch. 4.1 - Verify the following general solutions and find...Ch. 4.1 - Verify the following general solutions and find...Ch. 4.1 - Verify the following general solutions and find...Ch. 4.1 - Verify the following general solutions and find...Ch. 4.1 - Verify the following general solutions and find...Ch. 4.1 - Verify the following general solutions and find...Ch. 4.1 - For the following problems, find the general...Ch. 4.1 - For the following problems, find the general...Ch. 4.1 - For the following problems, find the general...Ch. 4.1 - For the following problems, find the general...Ch. 4.1 - For the following problems, find the general...Ch. 4.1 - For the following problems, find the general...Ch. 4.1 - For the following problems, find the general...Ch. 4.1 - For the following problems, find the general...Ch. 4.1 - For the following problems, find the general...Ch. 4.1 - For the following problems, find the general...Ch. 4.1 - Solve the following initial-value problems...Ch. 4.1 - Solve the following initial-value problems...Ch. 4.1 - Solve the following initial-value problems...Ch. 4.1 - Solve the following initial-value problems...Ch. 4.1 - Solve the following initial-value problems...Ch. 4.1 - Solve the following initial-value problems...Ch. 4.1 - Solve the following initial-value problems...Ch. 4.1 - Solve the following initial-value problems...Ch. 4.1 - Solve the following initial-value problems...Ch. 4.1 - Solve the following initial-value problems...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.1 - Recall that a family of solutions includes...Ch. 4.2 - For the following problems, use the direction...Ch. 4.2 - For the following problems, use the direction...Ch. 4.2 - For the following problems, use the direction...Ch. 4.2 - For the following problems, use the direction...Ch. 4.2 - For the following problems, use the direction...Ch. 4.2 - For the following problems, use the direction...Ch. 4.2 - For the following problems, use the direction...Ch. 4.2 - For the following problems, use the direction...Ch. 4.2 - Draw the direction field for the following...Ch. 4.2 - Draw the direction field for the following...Ch. 4.2 - Draw the direction field for the following...Ch. 4.2 - Draw the direction field for the following...Ch. 4.2 - Draw the direction field for the following...Ch. 4.2 - Draw the directional field for the following...Ch. 4.2 - Draw the directional field for the following...Ch. 4.2 - Draw the directional field for the following...Ch. 4.2 - Draw the directional field for the following...Ch. 4.2 - Draw the directional field for the following...Ch. 4.2 - Match the direction field with the given...Ch. 4.2 - Match the direction field with the given...Ch. 4.2 - Match the direction field with the given...Ch. 4.2 - Match the direction field with the given...Ch. 4.2 - Match the direction field with the given...Ch. 4.2 - Match the direction field with the given...Ch. 4.2 - Match the direction field with the given...Ch. 4.2 - Match the direction field with the given...Ch. 4.2 - Match the direction field with the given...Ch. 4.2 - Match the direction field with the given...Ch. 4.2 - Estimate the following solutions using Euler’s...Ch. 4.2 - Estimate the following solutions using Euler’s...Ch. 4.2 - WEstimate the following solutions using Euler’s...Ch. 4.2 - Estimate the following solutions using Euler’s...Ch. 4.2 - Estimate the following solutions using Euler’s...Ch. 4.2 - Estimate the following solutions using Euler’s...Ch. 4.2 - Estimate the following solutions using Euler’s...Ch. 4.2 - Estimate the following solutions using Euler’s...Ch. 4.2 - Estimate the following solutions using Euler’s...Ch. 4.2 - Estimate the following solutions using Euler’s...Ch. 4.2 - Differential equations can be used to model...Ch. 4.2 - Differential equations can be used to model...Ch. 4.2 - Differential equations can be used to model...Ch. 4.2 - Differential equations can be used to model...Ch. 4.2 - Differential equations can be used to model...Ch. 4.2 - Differential equations can be used to model...Ch. 4.2 - Differential equations can be used to model...Ch. 4.2 - Differential equations can be used to model...Ch. 4.2 - Differential equations can be used to model...Ch. 4.2 - Differential equations can be used to model...Ch. 4.2 - Consider the initial-value problem y' = 2y, y(0) =...Ch. 4.2 - Consider the initial-value problem y' = 2y, y(0) =...Ch. 4.2 - Consider the initial-value problem y' = 2y, y(0) =...Ch. 4.2 - Consider the initial-value problem y' = 2y, y(0) =...Ch. 4.2 - Consider the initial-value problem y' = 2y, y(0) =...Ch. 4.3 - Solve the following initial-value problems with...Ch. 4.3 - Solve the following initial-value problems with...Ch. 4.3 - Solve the following initial-value problems with...Ch. 4.3 - Solve the following initial-value problems with...Ch. 4.3 - Find the general solution to the differential...Ch. 4.3 - Find the general solution to the differential...Ch. 4.3 - Find the general solution to the differential...Ch. 4.3 - Find the general solution to the differential...Ch. 4.3 - Find the general solution to the differential...Ch. 4.3 - Find the general solution to the differential...Ch. 4.3 - Find the general solution to the differential...Ch. 4.3 - Find the general solution to the differential...Ch. 4.3 - Find the general solution to the differential...Ch. 4.3 - Find the general solution to the differential...Ch. 4.3 - Find the solution to the initial-value problem....Ch. 4.3 - Find the solution to the initial-value problem....Ch. 4.3 - Find the solution to the initial-value problem....Ch. 4.3 - Find the solution to the initial-value problem....Ch. 4.3 - Find the solution to the initial-value problem....Ch. 4.3 - Find the solution to the initial-value problem....Ch. 4.3 - Find the solution to the initial-value problem....Ch. 4.3 - Find the solution to the initial-value problem....Ch. 4.3 - Find the solution to the initial-value problem....Ch. 4.3 - Find the solution to the initial-value problem....Ch. 4.3 - For the following problems, use a software program...Ch. 4.3 - For the following problems, use a software program...Ch. 4.3 - For the following problems, use a software program...Ch. 4.3 - For the following problems, use a software program...Ch. 4.3 - For the following problems, use a software program...Ch. 4.3 - Most drugs in the bloodstream decay according to...Ch. 4.3 - A drug is administered intravenously to a patient...Ch. 4.3 - [T] How often should a drug be taken if its dose...Ch. 4.3 - A tank contains 1 kilogram of salt dissolved in...Ch. 4.3 - A tank containing 10 kilograms of salt dissolved...Ch. 4.3 - [T] For the preceding problem, find flow much salt...Ch. 4.3 - Torricelli’s law states that for a water tank with...Ch. 4.3 - For the preceding problem, determine how long it...Ch. 4.3 - For the following problems, use Newton’s law of...Ch. 4.3 - For the following problems, use Newton’s law of...Ch. 4.3 - For the following problems, use Newton’s law of...Ch. 4.3 - For the following problems, use Newton’s law of...Ch. 4.3 - For the following problems, use Newton’s law of...Ch. 4.3 - For the following problems, use Newton’s law of...Ch. 4.3 - For the following problems, use Newton’s law of...Ch. 4.3 - For the following problems, use Newton’s law of...Ch. 4.3 - For the following problems, use Newton’s law of...Ch. 4.3 - For the following problems, use Newton’s law of...Ch. 4.3 - For the following problems, use Newton’s law of...Ch. 4.3 - For the following problems, use Newton’s law of...Ch. 4.4 - Student Project: Logistic Equation with a...Ch. 4.4 - Student Project: Logistic Equation with a...Ch. 4.4 - Student Project: Logistic Equation with a...Ch. 4.4 - Student Project: Logistic Equation with a...Ch. 4.4 - For the following problems, consider the logistic...Ch. 4.4 - For the following problems, consider the logistic...Ch. 4.4 - For the following problems, consider the logistic...Ch. 4.4 - For the following problems, consider the logistic...Ch. 4.4 - For the following problems, consider the logistic...Ch. 4.4 - A population of deer inside a park has a carrying...Ch. 4.4 - A population of frogs in a pond has a growth rate...Ch. 4.4 - [T] Bacteria grow at a rate of 2O per hour in a...Ch. 4.4 - [T] Rabbits in a park have an initial population...Ch. 4.4 - [T] Two monkeys are placed on an island. After 5...Ch. 4.4 - [T] A butterfly sanctuary is built that can hold...Ch. 4.4 - The following problems consider the logistic...Ch. 4.4 - The following problems consider the logistic...Ch. 4.4 - The following problems consider the logistic...Ch. 4.4 - The following problems consider the logistic...Ch. 4.4 - The following problems consider the logistic...Ch. 4.4 - It is more likely that the amount of fishing is...Ch. 4.4 - It is more likely that the amount of fishing is...Ch. 4.4 - It is more likely that the amount of fishing is...Ch. 4.4 - It is more likely that the amount of fishing is...Ch. 4.4 - It is more likely that the amount of fishing is...Ch. 4.4 - The following problems add in a minimal threshold...Ch. 4.4 - The following problems add in a minimal threshold...Ch. 4.4 - The following problems add in a minimal threshold...Ch. 4.4 - The following problems add in a minimal threshold...Ch. 4.4 - The following problems add in a minimal threshold...Ch. 4.4 - The following questions consider the Gompertz...Ch. 4.4 - The following questions consider the Gompertz...Ch. 4.4 - The following questions consider the Gompertz...Ch. 4.4 - The following questions consider the Gompertz...Ch. 4.4 - The following questions consider the Gompertz...Ch. 4.4 - The following questions consider the Gompertz...Ch. 4.4 - The following questions consider the Gompertz...Ch. 4.4 - The following questions consider the Gompertz...Ch. 4.4 - The following questions consider the Gompertz...Ch. 4.4 - Below is a table of the populations of whooping...Ch. 4.4 - Below is a table of the populations of whooping...Ch. 4.4 - Below is a table of the populations of whooping...Ch. 4.4 - Below is a table of the populations of whooping...Ch. 4.4 - Below is a table of the populations of whooping...Ch. 4.5 - Are the following differential equations linear?...Ch. 4.5 - Are the following differential equations linear?...Ch. 4.5 - Are the following differential equations linear?...Ch. 4.5 - Are the following differential equations linear?...Ch. 4.5 - Are the following differential equations linear?...Ch. 4.5 - Write the following first-order differential...Ch. 4.5 - Write the following first-order differential...Ch. 4.5 - Write the following first-order differential...Ch. 4.5 - Write the following first-order differential...Ch. 4.5 - Write the following first-order differential...Ch. 4.5 - What are the integrating factors for the following...Ch. 4.5 - What are the integrating factors for the following...Ch. 4.5 - What are the integrating factors for the following...Ch. 4.5 - What are the integrating factors for the following...Ch. 4.5 - What are the integrating factors for the following...Ch. 4.5 - Solve the following differential equations by...Ch. 4.5 - Solve the following differential equations by...Ch. 4.5 - Solve the following differential equations by...Ch. 4.5 - Solve the following differential equations by...Ch. 4.5 - Solve the following differential equations by...Ch. 4.5 - Solve the following differential equations by...Ch. 4.5 - Solve the following differential equations by...Ch. 4.5 - Solve the following differential equations by...Ch. 4.5 - Solve the following differential equations by...Ch. 4.5 - Solve the following differential equations by...Ch. 4.5 - Solve the following differential equations. Use...Ch. 4.5 - Solve the following differential equations. Use...Ch. 4.5 - Solve the following differential equations. Use...Ch. 4.5 - Solve the following differential equations. Use...Ch. 4.5 - Solve the following differential equations. Use...Ch. 4.5 - Solve the following differential equations. Use...Ch. 4.5 - Solve the following differential equations. Use...Ch. 4.5 - Solve the following differential equations. Use...Ch. 4.5 - Solve the following initial-value problems by...Ch. 4.5 - Solve the following initial-value problems by...Ch. 4.5 - Solve the following initial-value problems by...Ch. 4.5 - Solve the following initial-value problems by...Ch. 4.5 - Solve the following initial-value problems by...Ch. 4.5 - Solve the following initial-value problems by...Ch. 4.5 - Solve the following initial-value problems by...Ch. 4.5 - Solve the following initial-value problems by...Ch. 4.5 - Solve the following initial-value problems by...Ch. 4.5 - Solve the following initial-value problems by...Ch. 4.5 - A falling object of mass m can reach terminal...Ch. 4.5 - Using your expression from the preceding problem,...Ch. 4.5 - [T] Using your equation for terminal velocity,...Ch. 4.5 - A more accurate way to describe terminal velocity...Ch. 4.5 - Using your expression from the preceding problem,...Ch. 4.5 - [T] Using your equation for terminal velocity,...Ch. 4.5 - For the following problems, determine how...Ch. 4.5 - For the following problems, determine how...Ch. 4.5 - For the following problems, determine how...Ch. 4.5 - For the following problems, determine how...Ch. 4.5 - For the following problems, determine how...Ch. 4 - True or False? Justify your answer with a proof or...Ch. 4 - True or False? Justify your answer with a proof or...Ch. 4 - True or False? Justify your answer with a proof or...Ch. 4 - True or False? Justify your answer with a proof or...Ch. 4 - For the following problems, find the general...Ch. 4 - For the following problems, find the general...Ch. 4 - For the following problems, find the general...Ch. 4 - For the following problems, find the general...Ch. 4 - For the following problems, find the general...Ch. 4 - For the following problems, find the general...Ch. 4 - For the following problems, find the solution to...Ch. 4 - For the following problems, find the solution to...Ch. 4 - For the following problems, find the solution to...Ch. 4 - For the following problems, find the solution to...Ch. 4 - For the following problems, find the solution to...Ch. 4 - For the following problems, find the solution to...Ch. 4 - For the following problems, draw the directional...Ch. 4 - For the following problems, draw the directional...Ch. 4 - For the following problems, use Euler’s Method...Ch. 4 - For the following problems, use Euler’s Method...Ch. 4 - For the following problems, set up and solve the...Ch. 4 - For the following problems, set up and solve the...Ch. 4 - For the following problems, set up and solve the...Ch. 4 - For the following problems, set up and solve the...Ch. 4 - For the following problems, set up and solve the...Ch. 4 - For the following problems, set up and solve the...Ch. 4 - For the following problems, set up and solve the...Ch. 4 - For the following problems, set up and solve the...Ch. 4 - For the following problems, set up and solve the...

Additional Math Textbook Solutions

Find more solutions based on key concepts
For the following exercises, determine whether the statement is true or false. Explain why. 101. A function of ...

Calculus Volume 1

Use the following information to answer the next seven exercises: A ballet instructor is interested in knowing ...

Introductory Statistics

Convert each of the following percents to decimals: 78%

Mathematics All Around (6th Edition)

Of the 1000 first-year students at a certain college, 700 take mathematics courses, 300 take mathematics and ec...

Finite Mathematics & Its Applications (12th Edition)

CHECK POINT 1 Find a counterexample to show that the statement The product of two two-digit numbers is a three-...

Thinking Mathematically (6th Edition)

CHECK POINT 1 Find a counterexample to show that the statement The product of two two-digit numbers is a three-...

Thinking Mathematically (7th Edition)

Knowledge Booster
Background pattern image
Math
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Text book image
Discrete Mathematics and Its Applications ( 8th I...
Math
ISBN:9781259676512
Author:Kenneth H Rosen
Publisher:McGraw-Hill Education
Text book image
Mathematics for Elementary Teachers with Activiti...
Math
ISBN:9780134392790
Author:Beckmann, Sybilla
Publisher:PEARSON
Text book image
Calculus Volume 1
Math
ISBN:9781938168024
Author:Strang, Gilbert
Publisher:OpenStax College
Text book image
Thinking Mathematically (7th Edition)
Math
ISBN:9780134683713
Author:Robert F. Blitzer
Publisher:PEARSON
Text book image
Discrete Mathematics With Applications
Math
ISBN:9781337694193
Author:EPP, Susanna S.
Publisher:Cengage Learning,
Text book image
Pathways To Math Literacy (looseleaf)
Math
ISBN:9781259985607
Author:David Sobecki Professor, Brian A. Mercer
Publisher:McGraw-Hill Education
SEE MORE TEXTBOOKS
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY
Solution of Differential Equations and Initial Value Problems; Author: Jefril Amboy;https://www.youtube.com/watch?v=Q68sk7XS-dc;License: Standard YouTube License, CC-BY