I am supposed to find a series solution for y''=y^2.
My problem is with the y^2. I've started with the following but then I get stuck:
y= sum(anx^n) and y''=sum(n*n-1)anx^n-2 and then I put these into the equation.
With the y^2 I end up with the multiplication of two series...I don't know if this is correct, and I don't know how to deal with the product of two series....
wow...that was fast. I've been working on this problem for 2 days. I have more questions if you are willing!
I am supposed to show that the solution of x' = 1 + z^4 + x^2
with x(0)=0 cannot be bounded for all z. I'm guessing I'm supposed to show that it doesn't satisfy a Lipschitz condition but I have no idea how to do that.
Thanks again...where have you been all my life.
Hello,
It is better to ask new questions in new threads...
Anyway, let f(z,x) such that :
Now you have to prove that f is Lipschitz wrt to x, uniformly to z.
So let's consider x and y. Does there exist a constant C such that ?
From the mean value theorem, we know that there exists such that :
So if you can't bound that partial derivative, then it's not a Lipschitz function.
And over , this is not bounded.