Concept explainers
To draw : the direction field using computer algebra system and sketch on it the solution curve that passes through the point.
Explanation of Solution
Given information :
The differential equation is
Graph :
By using computer algebra system,
The direction field is obtained as:
To sketch the solution curves first sketch the solution, for sketching solution start at the origin and move to the right in the direction of the line segment (which has slope 1), then continue the solution curve so that it moves parallel to the nearby line segments. And for more solution curve change the y -intercept.
Since solution graph passes through the point
So the graph can be observed as:
Using implicit plotting capability of a CAS to graph the curve
The graph can be obtained as :
Interpretation : from the above graph it can be observed that the graph by direction field and CAS are little bit different .
Chapter 7 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning