Originally Posted by

**aznmaven** Hi all,

The problem assigned to me was to show that the equation y'(t)==t^2+y(t)^2 has a solution for initial conditions y(0) = 0 over the interval 0<= t <= min(a, b/(a^2+b^2)), where we are considering a rectangle R, 0<= t <= a, -b<=y<=b.

What puzzles me is that the uniqueness and existence theorem says that if the DE is of the form y'(t) = f(t,y), where f and df/dy (partial derivative) are continuous over some rectangle containing the initial conditions (t0,y0) then the solution exists and is unique in that rectangle. In this case, f(t,y) is simply t^2 + y^2, and df/dy = 2 y. Both are clearly continuous for all values of t and y, so what is up with this question?