Thm: Suppose that both the function f(x,y) and its partial Derivative fy(x,y) are continuous on some rectangle R in the xy plane that contains the point (a,b) in its interior. Then, for some open interval I containing the point a, the initial value problem has one and only one solution that is defined on the interval I.
I have to determine if the above Thm does or does not guarantee existence of a solution of:
dy/dx = x lny ; y(1) = 1
Can someone show how this is done? Thanks a lot!!