Match the differential equation with its direction field. y' = 8(x + y) - 1 I -Q.31 +0,2 -0.1 0.1 -0,3 -0.2-0.1 0.4 - 0.2 0.3- -0.1. //// /// La.3 D-2 -1 -1 Give reasons for your answer. 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 = 8, 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 = 8, y' = 0. O y' = 8(x + y) - 1 = 0 on the line y = -x + 1/8, and y' = -1 on the line y = -x. O y' = 8(x + y) - 1 = 0 on the lines x = 0 and y = 8. O y' = 8(x + y) - 1 = 0 on the lines x = 0 and y = 0, and y'> o for o
Match the differential equation with its direction field. y' = 8(x + y) - 1 I -Q.31 +0,2 -0.1 0.1 -0,3 -0.2-0.1 0.4 - 0.2 0.3- -0.1. //// /// La.3 D-2 -1 -1 Give reasons for your answer. 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 = 8, 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 = 8, y' = 0. O y' = 8(x + y) - 1 = 0 on the line y = -x + 1/8, and y' = -1 on the line y = -x. O y' = 8(x + y) - 1 = 0 on the lines x = 0 and y = 8. O y' = 8(x + y) - 1 = 0 on the lines x = 0 and y = 0, and y'> o for o
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
Transcribed Image Text:Match the differential equation with its direction field.
y' = 8(x + y) – 1
y
y
y
y
15
15
0.3.
0.2
0.2
10
0,1F
0.1
--/ ///// /
---/ /// //
|-Q.3 +0,2 -0.1
0.1 - 0,2 /0,3
-0.3- -0,2
0.1
0,2 0,3
////
0.1
-
///// /////
-0.2
-6.2
//// /
//// /
// /// /////
++ X
+ H +++
+++ +H x
1
-1
2
-1
O-2
Give reasons for your answer.
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 = 8, 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 = 8, y' = 0.
%3D
O y' = 8(x + y) - 1 = 0 on the line y = -x + 1/8, and y' = -1 on the line y = -x.
O y' = 8(x + y) - 1 = 0 on the lines x = 0 and y = 8.
O y' = 8(x + y) - 1 = 0 on the lines x = 0 and y = 0, and y'> 0 for 0 <x < T/8, 0 < y < n/8.
%3D
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