Consider the equation of Example 5, (a) Does Theorem 1 imply the existen...

Consider the equation of Example 5,

(a) Does Theorem 1 imply the existence of a unique solution to (13) that satisfies y(x_o) = 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).