Problem 2.23. Heun's method (or improved Euler) is given by xm+1 = xm + / - ( (tm, xm) + f(tm+1, Ym)), Um = m + f(tm, Em)h. Show that using this method the error during one step is of O(h) (provided =C): h o(to + h) = xo + ((to, xo) + f(t, yo)) + O(h). Note that this is not the only possible scheme with this error order since h o(to + h) = xo +(f(t, xo) + f(to. yo)) + 0(h) as well.