Solving the Constant PDE ∂u/∂x=∂u/∂y

AlonsoMcLaren · May 25, 2013

∂u/∂x=∂u/∂y, can we ensure that u is a constant not dependent on x and y?

Simon Bridge · May 25, 2013

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"?

I like Serena · May 25, 2013

AlonsoMcLaren said:

∂u/∂x=∂u/∂y, can we ensure that u is a constant not dependent on x and y?

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.

Solving the Constant PDE ∂u/∂x=∂u/∂y

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Solving the Constant PDE ∂u/∂x=∂u/∂y

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