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: Existence of a unique solution?

  1. Oct 3, 2008 #1
    1. The problem statement, all variables and given/known data

    The theorem for a unique solution to a DE says: Let R be a rectangular region in the xy plane that contains the point (xo,yo). If f(x,y), which = dy/dx and the partial derivative of f(x,y) are continuous on R, then a unique solution exists in that region.

    Question: Determine a region of the xy plane for which the given differential equation would have a unique solution.

    dy/dx= x-y

    dy/dx= f(x,y)= x-y ,so f(x,y) is continuous on all reals for x & y

    then
    [tex]\partial[/tex]f/[tex]\partial[/tex]y = -1

    So this means that the solution is unique everywhere, right?
     
  2. jcsd
  3. Oct 3, 2008 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Yes, f and it's partial derivative are continuous everywhere. The solution is unique.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook