Differential Equations: Direction Fields

In summary, the conversation discusses sketching solution curves for the differential equation (dy/dx) = 2x + y through given points (0,-2) and (-1,3). The speaker also mentions the book "Fundamentals of Differential Equations 6th Edition" and a homework problem on Chapter 1.3, problem 2.
  • #1
anik18
11
0
(a) Sketch the solution curve that passes through (0,-2) in the direction field for (dy/dx)= 2x + y.

(b) Sketch the solution curve that passes through (-1,3) in the direction field for (dy/dx)= 2x + y.

(c) What can you say about the solution in part (b) as x approaches positive infinity? How about when x approaches negative infinity?


book: Fundamentals of Differential Equations 6th Edition by Nagle, Saff, and Snider
Chapter 1.3 and problem 2
 
Physics news on Phys.org
  • #2
Okay, what do you have for that?
 
  • #3
Anik, did you see the "sticky thread"? Homework problems should go the PF forum called "Homework", and you are expected to show some work.
 

1. What is a differential equation?

A differential equation is a mathematical equation that relates a function with its derivatives. It is used to model and describe relationships between changing quantities in various fields, such as physics and engineering.

2. What is a direction field?

A direction field is a graphical representation of a differential equation. It consists of a grid of small line segments that show the direction a solution curve would take at each point in the plane.

3. How do you draw a direction field?

To draw a direction field, you need to plot a grid of points on the plane and calculate the slope of the solution curve at each point. Then, you can draw a small line segment at each point in the direction of the calculated slope.

4. What information can be obtained from a direction field?

A direction field can provide information about the behavior of a solution curve for a given differential equation. It can also help identify critical points and determine the stability of solutions.

5. How are direction fields used in real-world applications?

Direction fields are used in various fields, such as physics, engineering, and economics, to model and analyze changing quantities. They can help predict and understand the behavior of systems and make informed decisions based on the information provided by the direction field.

Similar threads

  • Differential Equations
Replies
5
Views
438
  • Differential Equations
Replies
1
Views
1K
  • Differential Equations
Replies
1
Views
1K
  • Differential Equations
Replies
16
Views
814
  • Differential Equations
Replies
2
Views
916
  • Differential Equations
Replies
3
Views
1K
  • Differential Equations
2
Replies
52
Views
523
  • Differential Equations
Replies
5
Views
1K
  • Differential Equations
Replies
7
Views
2K
  • Differential Equations
Replies
5
Views
608
Back
Top