10. Consider the differential equation dy/dt = 2√yl. (a) Show that the function y(t) = 0 for all t is an equilibrium solution. (b) Find all solutions. [Hint: Consider the cases y > 0 and y < 0 separately. Then you need to define the solutions using language like "y(t) = ... when t ≤0 and y(t) = ... when t > 0."] (c) Why doesn't this differential equation contradict the Uniqueness Theorem?
10. Consider the differential equation dy/dt = 2√yl. (a) Show that the function y(t) = 0 for all t is an equilibrium solution. (b) Find all solutions. [Hint: Consider the cases y > 0 and y < 0 separately. Then you need to define the solutions using language like "y(t) = ... when t ≤0 and y(t) = ... when t > 0."] (c) Why doesn't this differential equation contradict the Uniqueness Theorem?
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For part c) why does our solutions y(t)=0 and y(t)=(t+c)^2 not contradict the uniquneness theorem?
![10. Consider the differential equation dy/dt = 2√yl.
(a) Show that the function y(t) = 0 for all t is an equilibrium solution.
(b) Find all solutions. [Hint: Consider the cases y > 0 and y < 0 separately. Then
you need to define the solutions using language like "y(t) = ... when t ≤0
and y(t) = ... when t > 0."]
(c) Why doesn't this differential equation contradict the Uniqueness Theorem?](https://content.bartleby.com/qna-images/question/652e5396-12b6-4e5e-865e-eecd6b9e3fee/30d8b027-a4c1-44dc-8dcc-fafc3186e025/ftkzk9_processed.png)
Transcribed Image Text:10. Consider the differential equation dy/dt = 2√yl.
(a) Show that the function y(t) = 0 for all t is an equilibrium solution.
(b) Find all solutions. [Hint: Consider the cases y > 0 and y < 0 separately. Then
you need to define the solutions using language like "y(t) = ... when t ≤0
and y(t) = ... when t > 0."]
(c) Why doesn't this differential equation contradict the Uniqueness Theorem?
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