A couple of questions/comments:
1. What was your answer to (c)?
2. Why not attempt a regular solution of the DE? It's first-order linear, right? You could at least get some sort of formula. What do you get?
Let , for .
(a)Show that satisfies a Lipschitz condition on with respect to . (Solved)
(b)Find the first 3 successive approximations , and of the initial value problem , . (Solved)
(c)State the largest interval in which a unique solution to the initial value problem in (b) is defined. (Solved)
(d)Let be the solution to the initial value problem in (b). Prove that , for all .
I've difficulty in doing the last questions. How do I go about doing the last question?
Thanks in advance.