First-order differential equations need not have unique solutions satisfying a given initial condition.

a)prove that there are infinitely many different solutions of the differential equations x- = x^1/3 satisfying x(0) = 0.

b)discuss the corresponding situation that occurs for x- = x/t, x(0) = x_0.

c)discuss the situation that occurs for x- = x/t^2, x(0) = 0.