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Definition of a linear differential equation

  1. Sep 13, 2008 #1
    1. The problem statement, all variables and given/known data
    Hi all. Is the following definition of a partial linear differential equation correct?


    A partial differential equation is called linear if no products of the function and/or its derivatives occur, and if the unknown function and its partial derivatives occur only to the first degree.


    I am a little worried about the "and/or" regarding products in the DE. Is it correct that the following term is NOT allowed in a linear differential equation?:

    [tex]
    \frac{\partial u}{\partial x}\frac{\partial u}{\partial t}
    [/tex]

    - and can you confirm the validity of the "and/or" in my definition? Thanks in advance.

    sincerely,
    Niles.
     
  2. jcsd
  3. Sep 17, 2008 #2
    Can anybody confirm this?

    And also: If I have a function f(x,y)*u, then is the equation still homogeneous and linear? As an example, take f(x,y)=cos(x):
     
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