21. Consider the initial value problem 3 y' = 2y = 3t+2e², 3t+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?
21. Consider the initial value problem 3 y' = 2y = 3t+2e², 3t+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?
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
100%
21
![the initial value problem
= 2 cos
y' + =y=
Find the coordinates of the first local maximum point of the solution
for t > 0.
N 18.
Consider the initial value problem
y' +
y=1-1/4, y(0) = yo.
the t-axis.
Find the value of yo for which the solution touches, but does not cross,
19. Consider the initial value problem
2 cost, y(0) = -1.
1
y + y = 3 + 2 cos(2t), y(0) = 0.
a. Find the solution of this initial value problem and describe its
behavior for large t.
N b. Determine the value of t for which the solution first
intersects the line y = 12.
20. Find the value of yo for which the solution of the initial value
problem
1000
JONES
y'
y' - y = 1 + 3 sint, y(0) = yo
remains finite as t → ∞.
21. Consider the initial value problem
-
3
y = 3t+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 → ∞?
22. Show that all solutions of 2y' + ty = 2 [equation (41) of the
text] approach a limit as t→∞, and find the limiting value.
Hint: Consider the general solution, equation (47). Show that the first
25.
All solut
26.
All solut
27. All solut
28. Variatio
solving the ger
a. If g(t
where A
b. If g(
equation
where A
differenti
c. Find
equation
in this m
techniqu
it is discu
order lin
In each of Pro
the given diff
29. y'-2y
30. y'+
y² + 1/3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7591feb6-6b8d-43e2-abaa-169c25d83a12%2F79243997-1d94-4d6f-a40f-82d9c864aad4%2Fgndftbi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:the initial value problem
= 2 cos
y' + =y=
Find the coordinates of the first local maximum point of the solution
for t > 0.
N 18.
Consider the initial value problem
y' +
y=1-1/4, y(0) = yo.
the t-axis.
Find the value of yo for which the solution touches, but does not cross,
19. Consider the initial value problem
2 cost, y(0) = -1.
1
y + y = 3 + 2 cos(2t), y(0) = 0.
a. Find the solution of this initial value problem and describe its
behavior for large t.
N b. Determine the value of t for which the solution first
intersects the line y = 12.
20. Find the value of yo for which the solution of the initial value
problem
1000
JONES
y'
y' - y = 1 + 3 sint, y(0) = yo
remains finite as t → ∞.
21. Consider the initial value problem
-
3
y = 3t+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 → ∞?
22. Show that all solutions of 2y' + ty = 2 [equation (41) of the
text] approach a limit as t→∞, and find the limiting value.
Hint: Consider the general solution, equation (47). Show that the first
25.
All solut
26.
All solut
27. All solut
28. Variatio
solving the ger
a. If g(t
where A
b. If g(
equation
where A
differenti
c. Find
equation
in this m
techniqu
it is discu
order lin
In each of Pro
the given diff
29. y'-2y
30. y'+
y² + 1/3
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