Answer and Step-by-step explanation:
Firstly, by definition, an interval of definition of any solution is the open interval on which it is defined.
Consider the problem p′=p², p(0)=1, has solution p(t) = 1/(1−t).
The definition of this solution is on the interval (−1/2,1/3), making it an interval of definition of solution.
However, it isn't the largest. The largest interval of definition is (−∞,1).
Consider another problem: p(t)=t√ satisfies the ODE p′=1/(2p).
Meanwhile, when considered as the solution of the ODE above, the domain of square root is [0,∞), and the interval of definition is (0,∞).
But at t=0 the ODE makes no sense, so it would be wrong to assume that y satisfies the ODE in this case. Meanwhile, ODEs are generally considered only on open intervals.
