1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Using initial conditions in a second order PDE

  1. Oct 20, 2011 #1
    1. The problem statement, all variables and given/known data

    I have a PDE for which i have found the general solution to be u(x,y) = f1(3x + t) + f2(-x + t)
    where f1 and f2 are arbitrary functions. I have initial conditions u(x,0) = sin (x) and partial derivative du/dt (x,0) = cos (2x)

    2. Relevant equations

    u(x,y) = f1(3x + t) + f2(-x + t)
    u(x,0) = sin (x)
    du/dt (x,0) = cos (2x)

    3. The attempt at a solution

    I have substituted u(x,0) and du/dt (x,0) into the general solution which gives me;

    u(x,0) = f1(3x) + f2(-x) = sin (x)
    du/dt(x,0) = f1'(3x) + f2'(-x) = cos (2x)

    but i am unsure as to where to go from here

    Thanks for any help
  2. jcsd
  3. Oct 20, 2011 #2
    I'll use h and v:


    It's not hard to eliminate v'(-x) right?

    then you'd have a regular DE:


    but then you got that 3x in there. What about making a change of independent variable by letting u=3x then convert the DE from one in terms of x (the one above) into one involvind u by remembering:


    now make this substitution into the one involving x, get the one involving u, solve it, then wherever there is a u in the answer, replace it by 3x.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook