The one-dimensional wave equation is unusual for a partial differential equation in that a relatively simple general solution may be found. Defining new variables ξ ξ = x − − c t , η η = x + c t changes the wave equation into ∂ ∂ 2 u ∂ ∂ ξ ξ ∂ ∂ η η ( x , t ) = 0 , which leads to the general solution u ( x , t ) = F ( ξ ξ ) + G ( η η ) , or equivalently, u ( x , t ) = F ( x − − c t ) + G ( x + c t ) .