?31E the equation of Example 5, (a) Does Theorem 1 imply the existence of a unique solution to (13) that satisfies y(xo) = 0?(b) Show that when equation (13) can’t possibly have a solution in a neighborhood of x = x0 that satisfies y(x0) = 0.(c) Show that there are two distinct solutions to (13) satisfying y(0) = 0 (see Figure 1.4 on page 9).

Solution : Step 1 :In this problem we have to verify the existence of the uniqueness theorem.(a) in this we have to verify the existence of the uniqueness in the given equation.Given the equation is Theorem 1 states that “ consider the initial value problem , If f and are continuous function in some rectangle That contains the point then the initial value problem has a unique solution in some interval where is positive number.”Then find the existence of unique solution to satisfies Consider equation Converted into Then When , then and are not defined.Hence the theorem 1 cannot be applied.