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

(1) ,

(2) ,

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.

Regards,

crushingyen