11. Consider the differential equation dy dt = y (a) Show that the constant function yı(t) = 0 is a solution. (b) Show that there are infinitely many other functions that satisfy the differen- tial equation, that agree with this solution when t≤ 0, but that are nonzero when t > 0. [Hint: You need to define these functions using language like "y(t) = ... when t ≤0 and y(t) = ... when t > 0."] (c) Why doesn't this example contradict the Uniqueness Theorem?
11. Consider the differential equation dy dt = y (a) Show that the constant function yı(t) = 0 is a solution. (b) Show that there are infinitely many other functions that satisfy the differen- tial equation, that agree with this solution when t≤ 0, but that are nonzero when t > 0. [Hint: You need to define these functions using language like "y(t) = ... when t ≤0 and y(t) = ... when t > 0."] (c) Why doesn't this example contradict the Uniqueness Theorem?
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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For Part b, how do we set up our solution
![11. Consider the differential equation
dy
dt
=
y
(a) Show that the constant function yı(t) = 0 is a solution.
(b) Show that there are infinitely many other functions that satisfy the differen-
tial equation, that agree with this solution when t≤ 0, but that are nonzero
when t > 0. [Hint: You need to define these functions using language like
"y(t) = ... when t ≤0 and y(t) =... when t > 0."]
(c) Why doesn't this example contradict the Uniqueness Theorem?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F652e5396-12b6-4e5e-865e-eecd6b9e3fee%2F69455c1a-1e8d-4ade-81db-f8ef1783550b%2F4vdzuzl_processed.png&w=3840&q=75)
Transcribed Image Text:11. Consider the differential equation
dy
dt
=
y
(a) Show that the constant function yı(t) = 0 is a solution.
(b) Show that there are infinitely many other functions that satisfy the differen-
tial equation, that agree with this solution when t≤ 0, but that are nonzero
when t > 0. [Hint: You need to define these functions using language like
"y(t) = ... when t ≤0 and y(t) =... when t > 0."]
(c) Why doesn't this example contradict the Uniqueness Theorem?
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