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Ordinary differential equation

  1. Jun 3, 2005 #1
    what is the word ordinary mean? Why is it called so.

    Am i correct to say that the solution of a differential equation is got by
    integrating that equation.
     
  2. jcsd
  3. Jun 3, 2005 #2
    An ordinary differential equation has derivatives with respect to one variable.

    [tex]\frac{dy(x)}{dx} + x = 0 [/tex]

    Oridnary is there to separate it from partial differential equations, which have derivatives with respect to multiple variables.

    [tex] \frac{\partial y(t,x,z)}{\partial t}+\frac{\partial^2 y(t,x,z)}{\partial x^2} = z[/tex]
     
    Last edited: Jun 3, 2005
  4. Jun 3, 2005 #3

    dextercioby

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    Ordinary means that the derivatives involved are taken wrt the only variable the unknown function depends on.

    "Integrating",not literally on every occasion.But u can make an abuse of language and call solving an ODE/PDE "integrating" it.

    Daniel.
     
  5. Jun 3, 2005 #4

    Pyrrhus

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    Ordinary to differential equations with total differentials.

    Example of ODE

    [tex] x^2 \frac{d^2 y}{dt^2} + x \frac{dy}{dt} + 15 = 0 [/tex]

    There are a lot of methods to solve a differential equation...
     
  6. Jun 3, 2005 #5

    dextercioby

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    I would be very careful with total differentials,if i were you. :wink:

    Daniel.
     
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