Interval of Validity:
An interval of validity is the range in which a solution to our differential equation is valid. The equation must not have any ‘holes’ or ‘breaks’ in it and it must contain the initial condition.
We can use our initial condition
to find what our exact solution is, and find out what is our interval of validity
For an Initial Value Problem (IVP) of the form:
With initial value:
If both p(x) and g(x) are continuous functions on the interval
, with our initial condition
being within this interval, then there exists a unique solution to the IVP above.