Set y equal to zero and look at how the derivative behaves along the x-axis. Do the same for the y-axis by setting x equal to 0 Consider the curve in the plane defined by setting y = 0 -- this should correspond to the points in the picture where the slope is zero. Setting y equal to a constant other than zero gives the curve of points where the slope is that constant. These are called isoclines, and an be used to construct the direction field picture by hand. (2x + y) (2y) 2. y = 2y + x²e2x 1. y' = 3. y = e-*+ 2y 4. y = 2 sin(x) +1+y
Set y equal to zero and look at how the derivative behaves along the x-axis. Do the same for the y-axis by setting x equal to 0 Consider the curve in the plane defined by setting y = 0 -- this should correspond to the points in the picture where the slope is zero. Setting y equal to a constant other than zero gives the curve of points where the slope is that constant. These are called isoclines, and an be used to construct the direction field picture by hand. (2x + y) (2y) 2. y = 2y + x²e2x 1. y' = 3. y = e-*+ 2y 4. y = 2 sin(x) +1+y
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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Concept explainers
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Question
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Transcribed Image Text:A. Set y equal to zero and look at how the derivative behaves along the x-axis.
B. Do the same for the y-axis by setting x equal to 0
C. Consider the curve in the plane defined by setting y = 0 -- this should correspond to the points in the picture where the slope is zero.
D. Setting y equal to a constant other than zero gives the curve of points where the slope is that constant. These are called isoclines, and
can be used to construct the direction field picture by hand.
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1. y'=
(2x + y)
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(2y)
2. y' = 2y + x²e2x
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3. y = e-x + 2y
4. y = 2 sin(x) +1+y
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