Consider the initial value problem
, , where and are positive integers with no common factors.
(a) Show that there are an infinite number of solutions if .
(b) Show that there is a unique solution if .
I separated the equations and was trying to integrate but I couldn't figure out how to do this.
I tried to break it down by the definition of absolute value so that
That way, I would show that for both cases (1) and (2), parts (a) and (b) are valid. Is this okay to do, or is there a more appropriate method to solving this problem?
Thank you very much.