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

First order ODE problem

  1. May 4, 2008 #1
    Let be the first order ODE's

    [tex] y'(x)g(x)=0 [/tex] and [tex] y'(x)g(x)=\delta (x-a) [/tex]

    except when x=a the two equations are equal , however the solutions are very different

    [tex] y(x)=C [/tex] and [tex] y(x)= C+ \int dx \frac{\delta (x-a)}{g(x)} [/tex]

    or using the properties of Dirac delta [tex] y(x)=C+\frac{1}{g(a)} [/tex]

    the second equation depends on the form of g(x) whereas the first does not, however except at the point x=a the 2 ODE's are completely equal.
     
  2. jcsd
  3. May 4, 2008 #2

    HallsofIvy

    User Avatar
    Science Advisor

    Why are you saying the two solutions are different? You should be writing C for one and, say, C' for the other- the two constants are not necessarily the same. In fact, all you are saying is that C= C'+ 1/g(a). Which is perfectly reasonable since 1/g(a) is itself a constant.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook