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

a) This was proved to have a solution

b) This was proved not to have any unique solution

c) This was also proved not to have any unique solution

Step-by-step explanation:

The step by step explanation is as attached below

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents