1. ## PDE

$\displaystyle u(x,y) = B (3x - 2y)$

B is an arbitary function

find partial differentiation of u. Not including B

2. Originally Posted by harveyo
$\displaystyle u(x,y) = B (3x - 2y)$

B is an arbitary function

find partial differentiation of u. Not including B
$\displaystyle \frac{\partial u}{\partial x} = 3B$ .... (1)

$\displaystyle \frac{\partial u}{\partial y} = -2B$ .... (2)

At this level you should be able to combine these two equations in such a way as to eliminate B.

$\displaystyle dy/dx = \partial x / \partial y = 3B (3x-2y)/ 2B (3x-2y) = -3/2$

4. Originally Posted by harveyo

$\displaystyle dy/dx = \partial x / \partial y = 3B (3x-2y)/ 2B (3x-2y) = -3/2$

i have used the wrong formula here?

i should solve the above simultaneously?

5. Originally Posted by mr fantastic
$\displaystyle \frac{\partial u}{\partial x} = 3B$ .... (1)

$\displaystyle \frac{\partial u}{\partial y} = -2B$ .... (2)

At this level you should be able to combine these two equations in such a way as to eliminate B.
$\displaystyle 2\frac{\partial u}{\partial x} = 6B$ .... (1)

$\displaystyle 3\frac{\partial u}{\partial y} = -6B$ .... (2)

hence

$\displaystyle 2\frac{\partial u}{\partial x} + 3\frac{\partial u}{\partial y} = 0$