Maximal solution Interval ODE question

Susanne217

1. The problem statement, all variables and given/known data

Given an ODE

[tex]h(y(t)) \frac{dy}{dt} = q(t)[/tex]

How do I define the maximal solution of this equation?

According to my textbook for this course a maximal solution for the above problem if it cannot be obtained from another solution as a restriction to a smaller interval.

I have been looking through many textbooks both in the in Lib and on google books.

Is there anyone here who would explain maximal solution in layman terms to me?

I know howto solve most ODE's and IVP and some BVP. But is the max interval of solution just the interval on which the solution of the ODE is defined?