Match the differential equation with its direction field. y ′ = 8 − y Give reasons for your answer. y ′ = 8 − y = 0 on the line y = −x + 1 8, and y ′ = −1 on the line y = −x. The slopes at each point are independent of x, so the slopes are the same along each line parallel to the x-axis. Note that for y = 8,
Match the differential equation with its direction field. y ′ = 8 − y Give reasons for your answer. y ′ = 8 − y = 0 on the line y = −x + 1 8, and y ′ = −1 on the line y = −x. The slopes at each point are independent of x, so the slopes are the same along each line parallel to the x-axis. Note that for y = 8,
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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Question
Match the differential equation with its direction field.
y ′ = 8 − y
Give reasons for your answer.
y ′ = 8 − y = 0
on the line
y = −x +
,
and
| 1 |
| 8 |
y ′ = −1
on the line
y = −x.
The slopes at each point are independent of x, so the slopes are the same along each line parallel to the x-axis. Note that for
y = 8,
y ′ = 0.
y ′ = 8 − y = 0
on the lines
x = 0
and
y = 0,
and
y ′ > 0
for
0 < x <
,
| ? |
| 8 |
0 < y <
.
The slopes at each point are independent of y, so the slopes are the same along each line parallel to the y-axis. Note that for
| ? |
| 8 |
y = 8,
y ′ = 0.
y ′ = 8 − y = 0
on the lines
x = 0
and
y = 8.
choose one pls
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