Consider the problem i f(x); x(0) = Xo with f e C1(2), 12 an open set in R. Denote the maximal solution by Pt(x0). We showed in lecture that 0+(x0) is differentiable in the variable to. For this homework (which I thought I had put in Resources on Thursday) I would like you to show that this derivative 04(x) is jointly continuous in (t, x). (I am reverting back to 04(x) rather than D+(2).) You will probably need to know something like sup ||04(x)||