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Help with basic pde

  1. Sep 21, 2008 #1
    http://mathbin.net/906

    cant figure this one out
     
  2. jcsd
  3. Sep 21, 2008 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi jomomma! Welcome to PF! :smile:

    (type "tex" instead of "EQ" on this forum :wink:)

    What have you tried?:smile:
     
  4. Sep 21, 2008 #3

    HallsofIvy

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    Staff Emeritus
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    What do you mean by "figure this out"? Did you stare at it expecting the answer to suddenly pop into your head or did you DO something like writing down the equations of the characteristics?

    If the latter, please show us what you did!
     
  5. Sep 21, 2008 #4
    I tried doin characteristics but i am getting confused with the [tex]u_z[/tex] term. Heres what i do

    [tex]

    \[
    \frac{dx}{dt}&=&x\Rightarrow x=x_0e^t
    \]
    \[
    \frac{dy}{dt}&=&2y\Rightarrow y=y_0e^2t
    \]
    \[
    \frac{dz}{dt}&=&1\Rightarrow z=z_0 + t
    \]
    \[
    \frac{du}{dt}&=&3u\Rightarrow u=u_0e^3t
    \]

    [/tex]

    from there i try to put [tex]y[/tex] and [tex]x[/tex] in to the equation for [tex]u[/tex]

    [tex]
    u=xy=x_0y_0e^3t
    [/tex]

    what do i do with [tex]z[/tex] and [tex]\varphi(x,y)[/tex]
     
    Last edited: Sep 21, 2008
  6. Sep 23, 2008 #5
    could someone verify whether the correct answer is

    [tex]

    u(x,y,z)=\varphi(xe^{-z},ye^{-2z})e^{3z}

    [/tex]
     
  7. Sep 23, 2008 #6
    Can't you plug it in and check like you would with any DE?
     
  8. Sep 23, 2008 #7
    yes, i can and i have, but i wanted third party confirmation, because i may not have included all solutions or may have made a mistake
     
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