Example: Sketch the direction field for the equation y' = y – t over the square -2 < t, y < 2, then using this direction field sketch the solution that passes through the points (-1,±1).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
Example: Sketch the direction field for the equation y' = y – t over the
square -2 < t, y < 2, then using this direction field sketch the solution that
passes through the points (-1,±1).
Transcribed Image Text:Example: Sketch the direction field for the equation y' = y – t over the square -2 < t, y < 2, then using this direction field sketch the solution that passes through the points (-1,±1).
Expert Solution
Step 1

The direction field is a graph of small line segments passing through various points whose slope is equal to the value of the differential equation at that point. 

For -2t,y2, the direction field of the differential equation y'=ft, y=y-t along with two solutions (curves in red) passing through the points -1, -1 and -1, 1 is 

steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Knowledge Booster
Implicit Differentiation
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,