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Simple partial differential equation

  1. May 1, 2012 #1
    Hello.

    I have equation:

    [tex]\frac{\partial T}{\partial t}-\frac{1}{2}\cdot \frac{(\partial)^2 T}{\partial x^2}=0[/tex]

    I calculated determinant:

    [tex]\Delta=(-\frac{1}{2})^2)-4\cdot 1 \cdot 0 \Rightarrow \sqrt{\Delta}=\frac{1}{2} \\ (\frac{dT}{dt})_{1}=-\frac{1}{4} \\ (\frac{dT}{dt})_{2}=\frac{1}{4}[/tex]

    next

    [tex]T=-\frac{1}{4}t+C_{1} \Rightarrow T+\frac{1}{4}t=C_{1} \\ T=\frac{1}{4}t+C_{2} \Rightarrow T-\frac{1}{4}t=C_{2}[/tex]

    I am add a new coefficients [tex]\eta[/tex] and [tex]\xi[/tex], then

    [tex]\xi=\frac{1}{4}t+T\\ \eta=-\frac{1}{4}t+T[/tex]

    Then I calculated matrix jacobian's =[tex]\frac{1}{2}[/tex]

    Good?

    I greet

    Post edited
     
    Last edited: May 2, 2012
  2. jcsd
  3. May 1, 2012 #2

    HallsofIvy

    User Avatar
    Science Advisor

    I'm not all that clear on what you are doing but that first statement is obviously untrue.
    [tex]\Delta= (-\frac{1}{2})^2- 4\cdot 1 \cdot 0= \frac{1}{4}[/tex]
    so
    [tex]\sqrt{\Delta}= \frac{1}{2}[/tex]
    not [itex]\sqrt{2}[itex]

     
  4. May 2, 2012 #3
    Thanks,

    Of course, I made mistake in write. I would like solve partial differential equation but I dont have experience. I edited my post.
     
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