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Partial Differential Equation? What is this?

  1. Apr 14, 2008 #1
    The professor passed this out today for homework and I have no idea how to even get started. If someone could tell me what type of problem this is I could look it up in the textbook but I can't find anything similar. I couldn't figure out how to insert all of the symbols so I attached the problem as a .gif
     

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  2. jcsd
  3. Apr 15, 2008 #2

    HallsofIvy

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    What exactly is your problem? The paper leads you step by step through the solution. It says

    "Seeking a solution of the form u= f(x) cos([itex]\omega[/itex]t)+ g(x) sin([itex]\omega[/itex]t), show that ...."

    Okay, put that into the differential equation and see what must be true of f and g in order to satisfy the equation.
     
    Last edited: Apr 15, 2008
  4. Apr 21, 2008 #3
    I have been trying to figure out this problem for a week now and I am still drawing a blank on how to "put that into the differential equation." How exactly can I get started on this?
     
  5. Apr 22, 2008 #4

    HallsofIvy

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    Do you know how to "substitute" into an equation? The problem is askng you to substitute u= f(x) cos(t)+ g(x) sin(t) into the equation and tell what must be true of f and g in order to satisfy the equation.
     
  6. Apr 22, 2008 #5
    I'm not sure I understand exactly what you are talking about. What am I substituting u= f(x) cos(t)+ g(x) sin(t) into? The du/dt=D*(d2u/dx2) equation?
     
  7. Apr 22, 2008 #6

    HallsofIvy

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    Yes! That's the only equation you are given at that point!
     
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