Question

Let f1(x,y) and f2(x,y) be continuous in the domain D, and f1(x,y) < f2(x,y) for all (x,y) belongs to D, Let y1(x) and y2(x) be the solution of the DEs y1'= f1(x,y) and y2'= f2(x,y), respectively, existing in J=[x0, x0+a) such that y1(x0) < y2(x0).
Show that y1(x) < y2(x) for all x belongs to J.