Solution of an Ordinary Differential Equation

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.
 

Attachments

BTP

9
1
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?
The blurb could be a little bit clearer. When talking about a solution to a differential equation in a given problem the domain of interest is essential. The blurb implies this but it could be explained a bit more explicitly. So to answer your question, it is not a solution to a specific problem posed on [itex]I_1[/itex]. That you found a function that works on [itex]I_2[/itex] would satisfies a different problem, one posed on [itex]I_2[/itex].
 
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