Match the differential equation with its direction field. y' = 5(x + y) – 1 -0.6- --0.4 - -0.2 0.2 0.4 -0.6

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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9.2¢
Match the differential equation with its direction field.
y' = 5(x + y) - 1
/ 10
0.6
0.4
-0,6 --0.4- -0.2-
0.2 0.4 - -0.6
-0.4
o-2
Q,2
-Q.6|
+0,2
0.2 - 0.4 / /0,6
H Ht
o-2
-1
Give reasons for your answer.
O y' = 5(x + y) - 1 = 0 on the line y = -x + 1/5, and y' = -1 on the line y = -x.
O y' = 5(x + y) – 1 = 0 on the lines x = 0 and y = 0, and y' > o for 0 < x < T/5, 0 < y < T/5.
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 = 5, y' = 0.
O 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 = 5, y' = 0.
O y' = 5(x + y) – 1 = 0 on the lines x = 0 and y = 5.
Transcribed Image Text:9.2¢ Match the differential equation with its direction field. y' = 5(x + y) - 1 / 10 0.6 0.4 -0,6 --0.4- -0.2- 0.2 0.4 - -0.6 -0.4 o-2 Q,2 -Q.6| +0,2 0.2 - 0.4 / /0,6 H Ht o-2 -1 Give reasons for your answer. O y' = 5(x + y) - 1 = 0 on the line y = -x + 1/5, and y' = -1 on the line y = -x. O y' = 5(x + y) – 1 = 0 on the lines x = 0 and y = 0, and y' > o for 0 < x < T/5, 0 < y < T/5. 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 = 5, y' = 0. O 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 = 5, y' = 0. O y' = 5(x + y) – 1 = 0 on the lines x = 0 and y = 5.
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