Partial differential equations

**mel240** · January 18th 2011, 06:24 PM

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?

**dwsmith** · January 18th 2011, 06:32 PM

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.

**Danny** · January 19th 2011, 04:32 AM

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?

Thread: Partial differential equations

LinkBack

Thread Tools

Display

Partial differential equations

Similar Math Help Forum Discussions

Partial Differential Equations

partial differential equations

Partial Differential Equations

Partial Differential Equations

Partial Differential Equations

Search Tags