3 y' - ²y = 31+2e². = 3t+2e', y(0) = Yo-
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
21
![y +=y=2
y(0) = -1.
Find the coordinates of the first local maximum point of the solution
fort > 0.
N 18. Consider the initial value problem
cost,
= 2 cost,
2
y'
y² + = y = 1
²+²y=1-1/1
y(0) = Yo-
Find the value of yo for which the solution touches, but does not cross,
the t-axis.
19. Consider the initial value problem
y'
4
+y = 3+2 cos(21), y(0) = 0.
a. Find the solution of this initial value problem and describe its
behavior for large t.
Nb. Determine the value of t for which the solution first
intersects the line y = 12.
problem
20. Find the value of yo for which the solution of the initial value
y' - y = 1+3 sint, y(0) = yo
remains finite as t → ∞.
21. Consider the initial value problem
3
-->
2
y'.
-
= 31+2e', y(0) = Yo-
Find the value of yo that separates solutions that grow positively as
t → ∞ from those that grow negatively. How does the solution that
corresponds to this critical value of yo behave as t → ∞o?
22. Show that all solutions of 2y' + ty = 2 [equation (41) of the
text] approach a limit as too, and find the limiting valua
L
th](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F57991e4c-5884-4f1b-98b5-65190f7dc92c%2F61ad9668-5f8a-49cc-9b1b-c8636edc565d%2F95barr9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:y +=y=2
y(0) = -1.
Find the coordinates of the first local maximum point of the solution
fort > 0.
N 18. Consider the initial value problem
cost,
= 2 cost,
2
y'
y² + = y = 1
²+²y=1-1/1
y(0) = Yo-
Find the value of yo for which the solution touches, but does not cross,
the t-axis.
19. Consider the initial value problem
y'
4
+y = 3+2 cos(21), y(0) = 0.
a. Find the solution of this initial value problem and describe its
behavior for large t.
Nb. Determine the value of t for which the solution first
intersects the line y = 12.
problem
20. Find the value of yo for which the solution of the initial value
y' - y = 1+3 sint, y(0) = yo
remains finite as t → ∞.
21. Consider the initial value problem
3
-->
2
y'.
-
= 31+2e', y(0) = Yo-
Find the value of yo that separates solutions that grow positively as
t → ∞ from those that grow negatively. How does the solution that
corresponds to this critical value of yo behave as t → ∞o?
22. Show that all solutions of 2y' + ty = 2 [equation (41) of the
text] approach a limit as too, and find the limiting valua
L
th
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