11. Consider the differential equation dy dt (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 (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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