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?