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) = x0. (c) discuss the situation that occurs for x' = x/t^2, x(0) = 0. 1