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Homework Help: 2nd order differential equations I'm so screwed

  1. Jan 11, 2007 #1
    1. The problem statement, all variables and given/known data
    Uxx +u(x,y)=0


    2. Relevant equations
    ?


    3. The attempt at a solution

    Step 1) u(x,y)=A(x)B(y)
    Step 2) uxx=d^u/dx^2
    Step 3) d^u/dx^2 + A(x)B(y) = 0
    Step 4) d^u/dx^2 = -[A(x)B(y)] (?)

    I have no idea what I'm doing, so small words would be useful.
     
  2. jcsd
  3. Jan 11, 2007 #2

    HallsofIvy

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    You equation is uxx+ u(x,y)= 0?
    [tex]\frac{\partial^2u}{\partial x^2}+ u= 0[/tex]

    Since there is no differentiation with respect to y, just treat y as a constant. Can you solve u'+u= 0?
     
  4. Jan 11, 2007 #3
    Yeah I figured it out...it's Acosx+Bsinx...right? (I warned that I don't know what the heck I'm doing).
     
  5. Jan 11, 2007 #4

    dextercioby

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    Well, sort of, that form times an arbitrary function of y.

    Daniel.
     
  6. Jan 11, 2007 #5

    HallsofIvy

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    No, not "that form times an arbitrary function of y".

    Since y is being treated as a constant, the constants A and B may be functions of y: u(x,y)= f(y)cos(x)+ g(y)sin(x). That is not quite the same thing. For example, f(y)cos(x) satisfies the differential equation but is not a function of y times cos(x)+ sin(x).
     
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