Final answer:
A solution exists and is unique provided certain conditions are satisfied in an initial value problem.
Step-by-step explanation:
The question is asking about the existence and uniqueness of a solution to an initial value problem. In part (a), a solution exists if the initial conditions are satisfied, which means the function is defined for all values of t. So the correct condition is true. In part (b), a solution exists and is unique if the differential equation is well-defined and has a unique solution for every set of initial conditions. Therefore, the equations and initial conditions must satisfy certain conditions for a unique solution to exist. Without more information, we cannot determine if the condition given in (b) is correct or not.