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A very simple PDE

  1. May 25, 2013 #1
    ∂u/∂x=∂u/∂y, can we ensure that u is a constant not dependent on x and y?
  2. jcsd
  3. May 25, 2013 #2

    Simon Bridge

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    It says that the gradient of u in the x direction is the same as in the y direction for all (x,y).
    What sort of function has that property?

    What do you mean by "ensure"?
  4. May 25, 2013 #3

    I like Serena

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    The general solution is u(x,y)=f(x+y), where f is a differentiable function.
    So u can be dependent on x and y.
    For instance u=2(x+y) is a solution.
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