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.