Partial Differential Equation: Can f(u) Satisfy the Equation dz/dx - dz/dy = 0?

[jenuine]

Consider the partial differential equation 2dz/dx-dz/dy=0
Show that if f(u) is a differential function of one variable, then the partial differential equation is satisfied by z=f(x+2y)



3. The Attempt at a Solution : Change of variables? No idea :S

 

[HallsofIvy]

Here's a suggestion: DO WHAT IT SAYS! If z= f(x+ 2y), what is $\partial f/\partial x$? What is $\partial f/\partial y$? Let u= x+2y and use the chain rule.