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Consider the following partial differential equation for $u(x, y)$, with the constant $c > 1$:

$\dfrac{\partial u}{\partial y}+c\dfrac{\partial u}{\partial x}=0$

Solution of this equation is

  1. $u(x, y) = f (x+cy)$
  2. $u(x, y) = f (x-cy)$
  3. $u(x, y) = f (cx+y)$
  4. $u(x, y) = f (cx-y)$
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