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

A simple ODE I think

  1. Nov 23, 2011 #1

    lavinia

    User Avatar
    Science Advisor
    Gold Member

    dc/dx = x[itex]^{2}[/itex]e[itex]^{-xc}[/itex]
     
    lavinia, Nov 23, 2011
  2. jcsd
    Phys.org - latest science and technology news stories on Phys.org
  3. Nov 23, 2011 #2

    raymo39

    User Avatar

    ?? it doesnt seem too simple, first its non separable non linear, but it is only first order. not quite sure what the post is for
     
    raymo39, Nov 23, 2011
  4. Nov 23, 2011 #3

    Dickfore

    User Avatar

    Make the subst, [itex]u(x) \equiv x \, c(x)[/itex] and see what ODE you get for [itex]u(x)[/itex].
     
    Dickfore, Nov 23, 2011
  5. Nov 23, 2011 #4

    lavinia

    User Avatar
    Science Advisor
    Gold Member

    Hi Raymo I must apologise. The equationI wrote is wrong.

    The right equation is dc/dx = e[itex]^{-xc}[/itex]

    This solves for the y coordinate of a unit speed geodesic in the plane with a particular metric of constant negative curvature. The x coordinate is easy. Maybe a conformal change of coordinates would give an easier equation.
     
    lavinia, Nov 23, 2011
  6. Nov 24, 2011 #5

    Dickfore

    User Avatar

    This is not a correct hint for this equation.

    I think I found the way though. Solve your equation in terms of [itex]c[/itex]:

    [tex]
    \ln c' = - x \, c
    [/tex]

    [tex]
    c = -x \frac{1}{\ln p}, \ p \equiv c'(x)
    [/tex]

    Your equation becomes an implicit ODE of the D'Alemebert - Clauraut type. It is reduced to a linear ODE w.r.t. [itex]x = x(p)[/itex] after differentiating w.r.t. [itex]x[/itex].

    What differential equation do you get at this step? Can you perform the integral in a closed form using elementary functions?
     
    Dickfore, Nov 24, 2011
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: A simple ODE I think

  1. Help maximizing this functional please (it's simple, i think) (Replies: 0)

  2. A simple nonlinear ode (Replies: 13)

  3. A simple ODE problem (Replies: 10)

  4. An ODE I was thinking of. (Replies: 4)

  5. Simple ODE/PDE clarification (Replies: 2)

Loading...