In: Advanced Math
Suppose that f(t) is the unique solution to the IVP y' = t + y^2 , y(0) = 5 and g(t) is the unique solution to the IVP y' = 1/(y + t^2) , y(5) = 0.
a. Determine an IVP that the function y = f(g(t)) solves. [Hint: You differential equation part will contain the functions t, g(t), and y in its expression.
b. (2 points) Show that the function y = t also solves this IVP.
c. (2 points) Use the uniqueness part of the Existence & Uniqueness Theorem to conclude that f and g are inverses.