A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing


  • 3 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? is this right? Because 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. I don't know how to do the 2nd part.

  • This Question is Open
  1. anonymous
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    For this differential equation, it is non linear and first order. This means you need to use the existence and uniqueness theorem that goes like this. Call x dot f(x,t). If f and partial f/partial x is continuous on an interval containing 0 (the x knot), then there exists and unique solution to the IVP on an interval t-delta<t<t+delta where delta is a some positive number. You do not know delta, but it is not zero. I will draw the work. So f= 1+x^2 which is a polynomial and partial f/partial x is 2x which is a polynomial so they are continuous everywhere so there exists a solution within (0- delta, 0 + delta).

  2. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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...


  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.