Let f : R $\displaystyle \rightarrow$ R be differentiable and define u: $\displaystyle R^2$ $\displaystyle \rightarrow$$\displaystyle R$

by u(x,y) := $\displaystyle e^{x sin y}f(x - y)$ show that u satisfies the partial differential equation

$\displaystyle du/dx$ + $\displaystyle du/dy$= (sin y + x cos y)u ?