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Math Help - Help classifying DEs.

  1. #1
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    Help classifying DEs.

    Hi ..
    am A beginner At DEs
    I want to Know How i know that the equation is Ordinary or partial and whether its Linear Or Not ?!?
    Last edited by mr fantastic; June 21st 2010 at 02:15 PM. Reason: Edited title.
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  2. #2
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    Partial - Look for partial derivatives. None? Ordinary.
    Linear - Look for exponents other that "1" on any derivatives? None? Linear.
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  3. #3
    A Plied Mathematician
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    Technically, in the second part of TKHunny's admirably brief explanation, you have to include derivatives of zero order (i.e., the function itself), in considering whether the DE is linear or not. In addition, you have to check whether there are nonlinear functions being taken of any derivatives (zero on up). The simple pendulum equation, before the often-done small-angle approximation, is nonlinear, even though it doesn't have any derivatives (zero order on up) to any power other than 1, unless you include the power series expansion of the sin function.
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