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

A Derivatives of functions in ODE

  1. Apr 9, 2016 #1
    For ordinary differential equation
    [tex]y''(x)+V(x)y(x)+const y(x)=0[/tex]
    for which ##\lim_{x \to \pm \infty}=0## if we have that in some point ##x_0## the following statement is true
    ##y(x_0)=y'(x_0)=0## is then function ##y(x)=0## everywhere?
     
  2. jcsd
  3. Apr 10, 2016 #2
    I suppose you mean ## \lim_{x=\pm \infty} y(x) = 0 ##? And no the function doesn't have to be ## 0 ## everywhere. An example is ## y(x) = \tanh(x)^{2}(1-\tanh(x)^{2}) ##. (You will have to work out ## V(x) ## yourself.)
     
  4. Apr 10, 2016 #3
    Yes ##\lim_{x \to \pm \infty}y(x)=0##. Interesting example. Look here

    from 2:46 - 4:09.
     
  5. Apr 10, 2016 #4
    Well ## V(x) ## in the above solution is divergent in ## 0 ##. The product of ## V(x)y(x) ## still exists.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Derivatives of functions in ODE
Loading...