The solution of y'y = 2 is a relation that is not a function. %3D a Find the general solution of the DE. b Describe the family of curves you have found. c Draw the slope field for this DE. i Draw the solution curve that passes through the origin. ii Draw two other solution curves. iii Describe how your two solution curves can be obtained by simple transformations of the part i. iv What feature of the slope field makes this possible. d Evaluate the arbitrary constant, given that the curve passes through (0, 1). II
The solution of y'y = 2 is a relation that is not a function. %3D a Find the general solution of the DE. b Describe the family of curves you have found. c Draw the slope field for this DE. i Draw the solution curve that passes through the origin. ii Draw two other solution curves. iii Describe how your two solution curves can be obtained by simple transformations of the part i. iv What feature of the slope field makes this possible. d Evaluate the arbitrary constant, given that the curve passes through (0, 1). II
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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Part a and d on
Transcribed Image Text:11 The solution of y'y
= 2 is a relation that is not a function.
a Find the general solution of the DE.
b Describe the family of curves you have found.
c Draw the slope field for this DE.
i Draw the solution curve that passes through the origin.
ii Draw two other solution curves.
iii Describe how your two solution curves can be obtained by simple transformations of the c
part i.
iv What feature of the slope field makes this possible.
d Evaluate the arbitrary constant, given that the curve passes through (0, 1).
II
Transcribed Image Text:11 a y? = 4x + C
b Concave right parabolas with vertex on the x-axis.
// / /1 /
-३-२-11। { २ ३ १
X
+2
iii Shift left or right.
iv The isoclines are horizontal lines.
d y?
= 4x + 1
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