Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Interval of Definition

  1. Aug 22, 2010 #1
    What is interval of definition of a solution of a Differential Equation?
    How can we find the interval of definition of a differential equation?
    What are the properties of this interval?
    Is the solution of the DE and DE itself are continuous and differentiable on the interval?
     
  2. jcsd
  3. Aug 22, 2010 #2

    HallsofIvy

    User Avatar
    Science Advisor

    The interval of definition of a solution to a differential equation is the largest interval upon which is it "sufficiently" differentiable (a solution of a second order differential equation must be twice differentiable, etc.) from which is follows that it is continuous, and on which it satisfies the given differential equation.

    I'm not sure I have ever seen the phrase "interval of definition" applied to a differential equation itself before. But I will say that it doesn't make sense to talk about the equation itself being "continuous and differentiable". I assume you mean that the functions in the differential equation are differentiable. Again, "differentiable" implies "continuous" so it isn't necessary to say that.
     
  4. Aug 22, 2010 #3
    Dear Sir, if we are given an Initial value problem, say at x0, y=y0, then the interval of definition will be the largest interval containing the (x0,y0) on which the solution is "sufficiently differentiable. Am i right sir?
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook