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Homework Help: Answer need checking!

  1. Apr 28, 2006 #1
    I think I've solved this problem, but just need someone to check my answers.


    With initial data


    Use the method of charactersitics [tex]u(x,t)=u(\xi,\tau)[/tex], we get

    [tex]\tau_{t}=t[/tex], [tex]x_{u}=u[/tex] and [tex]u_{\tau}=2[/tex].

    So, by choice of our initial condition,

    [tex]\tau=t[/tex] and [tex]u=2t + f(\xi)[/tex].

    Since [tex]\xi=\xi(x,t)[/tex]. We have


    At [tex]t=0[/tex] we have [tex]u(x,0)=u(\xi(x,0),0)[/tex], therefore


    Since we do not know what [tex]f(x)[/tex] is, our solution for [tex]u(x,t)[/tex] is just


    with initial condition


    Is this right??
  2. jcsd
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