A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years ago
Show by verifying the hypothesis of the Existence and Uniqueness Theorem that the initial value problem x dot = 1+x^2, x(0) = 0 has a unique solution. Find the solution. what is the maximal interval of definition of the solution? I'll put what I think is the answer as a response. Could you tell me if I took the right approach?
 2 years ago
Show by verifying the hypothesis of the Existence and Uniqueness Theorem that the initial value problem x dot = 1+x^2, x(0) = 0 has a unique solution. Find the solution. what is the maximal interval of definition of the solution? I'll put what I think is the answer as a response. Could you tell me if I took the right approach?

This Question is Open

mathlilly
 2 years ago
Best ResponseYou've already chosen the best response.0Because f: R> R is continuous, then for any x knot which is an element of R, there is an interval (alpha,beta) containing 0 and there is a solution x(t) of x dot = f(x). The limit exist, therefore a solution exists. Because f is differentiable and f' is continuous, then x(t) is unique.

mathlilly
 2 years ago
Best ResponseYou've already chosen the best response.0The solution is 0 and the maximal interval of definition is (infinity,infinity)
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.