Hi,
the problem:
Use each of the three theorems in this section to predict where this problem has a solution, and then solve the problem explicitly, comparing the theory to the fact:
.
As stated in the problem, there are three theorems in my book dealing with existence and uniqueness of I.V.Ps.
The first one is a pure existence theorem and says;
If is continuous in a rectangle centered at , say
then the initial-value problem has a solution for , where is the maximum of in the rectangle .
Attempt:
For this problem, the rectangle is;
.
Hence is bounded by, .
Since is continuous, the I.V.P has a solution for .
Now, has a maximum when , so,
.
Assuming , we have that
.
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The explicit solutions is,
,
which is not defined if .
I can't say my prediction is very good...
Any suggestions are welcome, thanks.