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

Partial diffs help please!

  1. Aug 27, 2011 #1
    Show that under the transformation

    u=x, v=[itex]\alpha[/itex]x+[itex]\beta[/itex]t​
    Ayxx+Byxt+Cytt=0 ; B^2-4AC>0


    (A,B,C are constants)
    I have no idea where to start. and i have to present this problem to the front of my class on monday. Can anyone give me a big head start or anything?
  2. jcsd
  3. Aug 27, 2011 #2
    gotta' start taking partials. That's where to start.

    Is it like a bunch of people in there?

    Ok, just playing.

    So if y=f(x,t) and x=u and v=ax+bt, then:

    [tex]y_x=y_u u_x+y_v v_x[/tex]
    [tex]y_x=y_u+a y_v[/tex]

    but the second one is a litle tricky since you taking the partial of partials so:

    [tex]y_{xx}=\frac{\partial}{\partial x} \left(y_u+a y_v\right)=y_{uu} u_x+y_{vu} v_x+a\left(y_{uv}u_x+y_{vv} v_x\right)[/tex]

    Ok then, keep doing that for each partial in the first expression, make all those substitutions back into the first expression which wil turn it into an expression of y in terms of u and v, then simplify, cancel, whatever, and it should look like the second expression.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook