Understanding Partial Derivatives and the Wave Equation

[TheAntithesis]

Homework Statement

Let f = f(u,v) where u = x+y , v = x-y
Find f_{xx} and f_{yy} in terms of f_u, f_v, f_{uu}, f_{vv}, f_{uv}

Then express the wave equation \frac{\partial^2f}{\partial x^2} - \frac{\partial^2f}{\partial y^2} = 0

Homework Equations

Chain rule, product rule

The Attempt at a Solution

I've solved the partial derivatives f_{xx} = f_{uu) + 2f_{uv} + f_{vv} and f_{yy} = f_{uu) - 2f_{uv} + f_{vv}

So then \frac{\partial^2f}{\partial x^2} - \frac{\partial^2f}{\partial y^2} = 0 is not true unless f_{uv} = 0, how am I meant to express it?

 

[Ray Vickson]

Homework Statement

Let f = f(u,v) where u = x+y , v = x-y
Find f_{xx} and f_{yy} in terms of f_u, f_v, f_{uu}, f_{vv}, f_{uv}

Then express the wave equation \frac{\partial^2f}{\partial x^2} - \frac{\partial^2f}{\partial y^2} = 0

Homework Equations

Chain rule, product rule

The Attempt at a Solution

I've solved the partial derivatives f_{xx} = f_{uu) + 2f_{uv} + f_{vv} and f_{yy} = f_{uu) - 2f_{uv} + f_{vv}

So then \frac{\partial^2f}{\partial x^2} - \frac{\partial^2f}{\partial y^2} = 0 is not true unless f_{uv} = 0, how am I meant to express it?

You have just expressed it! f_{uv} = 0.

RGV

 

[TheAntithesis]

I was thinking it couldn't be that simple, apparently it is lol, thanks