Question

Let f(x,y) be continuous and satisfy the generalized Lipschitz condition;
|f(x,y1) - f(x,y2)| <= L(x) |y1 - y2| for all (x,y1), (x,y2) in S,
where the function L(x) is such that the integral from x0-a to x0+a of L(t) dt exixts.
Show that y'= f(x,y), y(x0)= y0 has at most one solution in |x-x0| <= a.