Hi, The definition (see attachment) says that f(x) is a solution to the differential equation if it satisfies the equation for every x in the interval. Assuming that I have a differential equation that I want to solve and the D.E. has an interval [itex]I_1[/itex], and I've come up a solution with an interval [itex]I_2[/itex], where [itex]I_2[/itex] is a subset of [itex]I_1[/itex], is it still a solution to the differential equation? If it isn't, does the solution still make sense? I'm new to differential equations and haven't solved anything DE yet.