Hello! Hope this post finds you all well!
When solving a problem, one may go through step(s) in which the domain
of the independent variable is restricted. When the final solution of the
problem is reached, this restriction may not seem to apply. My question
is if the domain restriction found still applies to the final solution.
As an example (I apologize for not having learned the typesetting program
syntax used in this forum - Tex or LaTex?):
In the linear DE y' + P(x)y = 0, the integrating factor has the form
exp[integral of P(x)]. I don't remember a specific instance offhand,
but found that the integrating factor involved the natural logarithm,
and thus was limited to a domain of x greater than zero. When the
final solution was reached, there was no restriction on this domain -
it happened that the domain was the entire x-axis.
Would the final solution still have the valid domain of x > 0 since the
integrating factor had that restriction?
expression mark-up language yet