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

- $u(x, y) = f (x+cy)$
- $u(x, y) = f (x-cy)$
- $u(x, y) = f (cx+y)$
- $u(x, y) = f (cx-y)$