- #1
kingwinner
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Homework Statement
Claim:
For the partial differential equation ∂u/∂x + ∂u/∂y = 0, the general solution is u(x,y) = f(x-y)
Homework Equations
N/A
The Attempt at a Solution
I remember that the number of arbitrary constants in the general solution should be the same as the order of the differential equation. For example, for 1st order ODEs, there should be one arbitrary constant in the general solution; for 2nd order ODEs, there should be two arbitrary constants in the general solution.
In this case, the order of the differential equation is one, so it should have one arbitrary constant in the general solution, right? However, the above claims that u(x,y) = f(x-y) is the general solution. I am puzzled...Where is the arbitrary constant?
Thanks for any help!