Chapter 1.5, Problem 4E

In Exercises 1—4, we refer to a function f, but we do not provide its formula. However, we do assume that f satisfies the hypotheses of the Uniqueness Theorem in the entire ty-plane, and we do provide various solutions to the given differential equation. Finally, we specify an initial condition. Using the Uniqueness Theorem, what can you conclude about the solution to the equation with the given initial condition?

4. $\frac{dy}{dt}=f\left(t,y\right)$
$y_1\left(t\right)=-1$ for all t is a solution.
$y_2\left(t\right)=1+t^2$ for all t is a solution.
initial condition y(0) = 1