Answer each question appropriately.If differentiable functions y = F(x) and y = G(x) both solve the initial value problem on an interval I, must for every x in I? Justify the answer.

Question

A. F(x) = G(x) for every x in I because integrating f(x) results in one unique function.
B. F(x) = G(x) for every x in I because when given an initial condition, we can find the integration constant when integrating f(x). Therefore, the particular solution to the initial value problem is unique.
C. F(x) and G(x) are not unique. There are infinitely many functions that solve the initial value problem. When solving the problem there is an integration constant C that can be any value. F(x) and G(x) could each have a different constant term.
D. There is not enough information given to determine if F(x) = G(x).

Answer 1

Answer: B