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

Answered: Example: Sketch the direction field for…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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

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