Differential Equations: Direction Fields

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The discussion focuses on sketching solution curves for the differential equation dy/dx = 2x + y, specifically for points (0,-2) and (-1,3). Participants are encouraged to analyze the behavior of the solution curve as x approaches both positive and negative infinity. The importance of showing work in homework submissions is emphasized, along with a reminder to post in the appropriate forum. The conversation highlights the need for understanding direction fields in relation to differential equations. Overall, the thread serves as a resource for students grappling with these concepts.
anik18
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(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
 
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Okay, what do you have for that?
 
Anik, did you see the "sticky thread"? Homework problems should go the PF forum called "Homework", and you are expected to show some work.
 

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