# Partial differential equations

• January 18th 2011, 07:24 PM
mel240
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?
• January 18th 2011, 07:32 PM
dwsmith
Quote:

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.
• January 19th 2011, 05:32 AM
Jester
Quote:

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?