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Here were given a linear first order differential equation with the initial condition y of negative two equals negative one. Were asked to find the interval in which the solution of the initial value problem above is certain to exist. So looking at our notes below, if we have a linear first order differential equation written in this form here with this initial condition if p of t and f of t are both continuous on an open interval from a to b, then there exists a unique solution for every t on the interval. And if we find all the intervals for which both p of t and f of t are continuous this is called the interval of validity. And if the interval contains t sub zero, which is the input value of the initial condition, then there exists a unique solution on the interval that satisfies the initial value problem. So to answer this question, well first find the interval of validity whichll be the intervals to which both p of t and f of t are continuous, and then well find the interval
