Quote by bilgek33
Thanks again for your interest, saltydog.
You are right there is typo there, but the result is the same. Here is the corrected one: http://www.people.virginia.edu/~bk5w...files/ode2.pdf
One another thing is f is between [0,1], which means it can be zero as well (when you wrote, you didn't include zero).
In terms of your question regarding uniqueness, to be honest, I don't know.
Any idea what to do when f is not 1 ??

I don't know either about what happens to uniqueness and it's becomming a very interesting problem for me: If g(t,y,y') and its partials are continuous at a point then we can be assured of a unique solution about the point. However, the proof of such I am familiar with makes no comment about uniqueness if they are not continuous.
I don't know what to do if f is not 1. Working it numerically "close to zero" is unacceptable to you right?
Maybe/hopefully someone else here more knowledgeable than I will post a comment and we can both learn.