How to find the lower and upper bound of a solution of a Cauchy problem? I am studying some diff

Paula Boyer

Paula Boyer

Answered question

2022-04-20

How to find the lower and upper bound of a solution of a Cauchy problem?
I am studying some differential equations especially the Cauchy problems, and I encountered this question:
(E):{y=ysin2(y)y(0)=x0
They supposed that 0<x0<π, and I have to find the upper and lower bounds of the solution, knowing that it is a maximal solution. I don't know where to start. I need some kind of help.

Answer & Explanation

eslasadanv3

eslasadanv3

Beginner2022-04-21Added 20 answers

Explanation:
From f(y)=ysin2(y) you know that f(0)=f(π)=0 with f(y)>0 inside that interval, and that this function is locally Lipschitz.
This is all you need to know to solve this task.

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