1. The problem statement, all variables and given/known data Find the largest open rectangle in the ty-plane that contains the initial value point and satisfies the following theorem: Let R be the open rectangle defined by a<t<b, α<y<β. Let f(t,y) be a function of two variables defined on R where f(t,y) and the partial derivative ∂f/∂y are continuous on R. Suppose (t0, y0) is a point in R. Then there is an open interval t-interval (c,d) contained in (a, b) and containing t0, in which there exists a unique solution of the initial value problem y'f(t,y), y(t0) = y0 (t-a)(t-3)y'= 1+ sec(y) and y(π)=1 2. Relevant equations 3. The attempt at a solution So, when I take the partial derivative I get ∂f(t,y)/∂y = [sec(y)tan(y)](t-1)(t-3)/(t-1)(t-3)2 From this I can see that: t≠1 t≠3 But y is available for all values. Hence the largest rectangle goes from 1 to 3 on the t axis and from -∞ to +∞ on the y axis. But this doesn't contain the initial value point. Am i missing something?