Consider the following partial differential equation u(x,

Consider the following partial differential equation u(x, y) with the constant c > 1:
δu + c δu = 0
δy δx

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)

u = f (x – cy)

	δu	= f' (x - cy)(1)
	δx

	δu	= f' (x - cy)(-c)
	δx

= –c. f¹ (x–cy)

= - c .	δu
	δx

∴	δu	+ c	δu	= 0
	δy		δx