1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Diff Equations: Theorem of Uniqueness

  1. Aug 14, 2011 #1
    1. The problem statement, all variables and given/known data

    Check if the given initial value is a unique solution.

    2. Relevant equations

    y'=y^(1/2), y(4)=0

    3. The attempt at a solution

    I got y(t)=(t/2)^2 and 0 at t=4

    So, we have two solutions to i.v.p.; therefore, it's not a unique solution.

    Is it correct?
  2. jcsd
  3. Aug 14, 2011 #2


    User Avatar
    Science Advisor

    I have no idea what you mean by "y(t)= (t/2)^2 and 0 at t= 4". If you mean "y(t)= (t/2)^2 if t is not 4, y(4)= 0", it is not a solution because it is not differentiable at t= 4. If you mean that y(t)= (t/2)^2 is one solution and y= 0 for all t is another solution, that is not correct because y(t)= (t/2)^2 give y(4)= 4, not 0. Please show exactly what the problem said and what you have tried to do.
  4. Aug 14, 2011 #3
    I guess I needed to mention about theorem of uniqueness. f=y^(1/2) and its partial derivative 1/2(root of y) are continuous except where y<=0. We can take any rectangle R containing the initial value point (4,0). Then the hypothesis of theorem of uniqueness is satisfied. How about this way???
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook