Explanation Given: The differential equation is as below. y ' = y − 2 x . Calculation: Substitute ( − 2 ) for x and ( − 2 ) for y in equation y ' = y − 2 x , y ' = y − 2 x = ( − 2 ) − 2 ( − 2 ) = − 2 + 4 = 2 The values of slopes for the variables x and y for the differential equation y ' = y − 2 x is tabulated in the below table. x y y ' = y − 2 x –2 –2 2 –2 2 6 2 2 –2

8th Edition

ISBN: 9781285741550

Author: James Stewart

Publisher: Cengage Learning

See similar textbooks

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…

Videos

Question

Chapter 9.2, Problem 11E

To determine

To sketch: The direction field of the differential equation y'=y−2x and find the curve that passes through the point (1,0).

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.2, Problem 10E

Chapter 9.2, Problem 12E

Students have asked these similar questions

2. Consider the following: Prove that x, x2, and 1/x are the solutions to the homogeneous equation corresponding to x³y"" + x²y" + 2xy' + 2y = 2x4. b. use variation of parameters to find a particular solution and complete the general solution to the differential equation. I am interested in process. You may use a computer for integration, finding determinants and doing Kramer's.

3. A spring is stretched 6 in. by a mass that weighs 8 lb. The mass is attached to a dashpot mechanism that has a damping constant of 0.25 lb-sec./ft. and is acted on by an external force of 4 cos 2t lb. a. Set-up the differential equation and initial value problem for the system. b. Write the function in phase-amplitude form. C. Determine the transient solution to the system. Show your work. d. Determine the steady state of this system. Show your work. e. Is the system underdamped, overdamped or critically damped? Explain what this means for the system.

4. Suppose that you have a circuit with a resistance of 20, inductance of 14 H and a capacitance of 11 F. An EMF with equation of E(t) = 6 cos 4t supplies a continuous charge 60 to the circuit. Suppose that the q(0)= 8 V and the q'(0)=7. Use this information to answer the following questions a. Find the function that models the charge of this circuit. b. Is the circuit underdamped, overdamped or critically damped?

Chapter 9 Solutions

Calculus: Early Transcendentals

Ch. 9.1 - Show that y=23ex+e2x is a solution of the...Ch. 9.1 - Verify that y = t cos t t is a solution of the...Ch. 9.1 - (a) For what values of r does the function y = erx...Ch. 9.1 - (a) For what values of k does the function y = cos...Ch. 9.1 - Which of the following functions are solutions of...Ch. 9.1 - (a) Show that every member of the family of...Ch. 9.1 - (a) What can you say about a solution of the...Ch. 9.1 - (a) What can you say about the graph of a solution...Ch. 9.1 - A population is modeled by the differential...Ch. 9.1 - The Fitzhugh-Nagumo model for the electrical...

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The direction field of the differential equation y ' = y − 2 x and find the curve that passes through the point ( 1 , 0 ) .

Solution Summary: The author illustrates the direction field of the differential equation y'=y-2x and the curve that passes through the point.

Concept explainers

Videos

To sketch: The direction field of the differential equation y'=y−2x and find the curve that passes through the point (1,0).

Want to see the full answer?

Chapter 9 Solutions