If we write the DE as...
... we observe that for the partial derivative has a singularity and the the Lipschitz aren't satisfied. As consequence of that the IVP...
... has more that one solution, among them and ...
I'm trying to get my head around this whole Lipschitz condition business, and while I understand the principle, I'm having trouble understanding it mathematically. I have the example IVP:
y'(t) = t*sqrt(|y|)
Which with y(0) = 0, fails on IVP solvers. Apparently this can be explained in terms of a Lipschitz condition, but I haven't got a clue where to start proving it.
Any help would be greatly appreciated.