# Math Help - Partial differential equations

1. ## Partial differential equations

Given u(x,y) = ф(3x-2y)
(ф is an arbitrary function) find a PDE for u. Im just not sure how to start this question, any suggestions?

2. Originally Posted by mel240
Given u(x,y) = ф(3x-2y)
(ф is an arbitrary function) find a PDE for u. Im just not sure how to start this question, any suggestions?
I guess you could do something like this

$Au_{xx}+Bu_{yy}+Cu_{x}+Du_{y}+Fu=0$

A, B, C, D, E, F are constants.

3. Originally Posted by mel240
Given u(x,y) = ф(3x-2y)
(ф is an arbitrary function) find a PDE for u. Im just not sure how to start this question, any suggestions?
You'll notice that

$\dfrac{\partial u}{\partial x} = 3\phi'(3x-2y)$

$\dfrac{\partial u}{\partial y} = -2\phi'(3x-2y)$

Now, can you think of a linear combination of these two to give you zero?