Existence and Uniqueness
Let R be a rectangular region in the x-y plane defined by
that contains the point (x0 , y0) in its interior.
If f(x,y)
and δf/δy are continuous on R,
then there exists some interval I0: (x0-h, x0+h), h > 0,
contained in [a,b], and a
unique function y(x), defined on I0, that is a solution of the initial
value problem
dy/dx = f(x,y)
y(x0) = y0.