Match the differential equation with its direction field. y'- sin(10x) sin(10y) 20) -0.3 1-0.2 1 +0x1 6.1 0.2 0/3 0.3- --0.2 -04- 6.- 0.2 - -0.3 -0.3 Give reasons for your answer. 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 y = 10, y' = 0. y' - sin(10x) sin(10y) = 0 on the lines x = 0 and y = 0, and y' >0 for 0 < x < x/10, 0 < y < /10. 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 = 10, y' = 0. y' = sin(10x) sin(10y) = 0 on the lines x = 0 and y = 10. y' = sin(10x) sin(10y) = 0 on the line y = -x + 1/10, and y' = -1 on the line y = -x.
Match the differential equation with its direction field. y'- sin(10x) sin(10y) 20) -0.3 1-0.2 1 +0x1 6.1 0.2 0/3 0.3- --0.2 -04- 6.- 0.2 - -0.3 -0.3 Give reasons for your answer. 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 y = 10, y' = 0. y' - sin(10x) sin(10y) = 0 on the lines x = 0 and y = 0, and y' >0 for 0 < x < x/10, 0 < y < /10. 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 = 10, y' = 0. y' = sin(10x) sin(10y) = 0 on the lines x = 0 and y = 10. y' = sin(10x) sin(10y) = 0 on the line y = -x + 1/10, and y' = -1 on the line y = -x.
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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Transcribed Image Text:Match the differential equation with its direction field.
y' = sin(10x) sin(10y)
20)
-0.31 1-0.2 \ +0x1 \ \
0- - 0.2 / /03
-0.3-
0.2
-0.1
0.1
0.2
-0.3
-2
-1
1
-2
-1
1
0.3-
Give reasons for your answer.
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 y = 10, y' = 0.
o y' = sin(10x) sin(10y)
= 0 on the lines x = 0 and y = 0, and y' > 0 for 0 < x < n/10, 0 < y < n/10.
O 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 = 10, y' = 0.
o y' = sin(10x) sin(10y)
= 0 on the lines x = 0 and y = 10.
o y' = sin(10x) sin(10y) = 0 on the line y = -x + 1/10, and y' = -1 on the line y = -x.
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