Originally Posted by

**bugatti79** Hi folks,

p(x,y), q(x,y) and f(x,y) are known functions and p(x,y) is positive and continuously diferentiable. Write out the following in co-ordinate form and determine whether its hyperbolic, parabolic or elliptic.

Here is my attempy to write it in co-ordinate form...I dont think its right

Given $\displaystyle

\vec \nabla \cdot (p \vec\nabla u)+qu=f

$

$\displaystyle

\displaystyle \vec\nabla \cdotp(p(x,y)\frac{\partial u }{\partial x}i+p(x,y)\frac{\partial u }{\partial y}j)+q(x,y)u(x,y)=f(x,y)

$

$\displaystyle

\displaystyle p(x,y)(\frac{\partial}{\partial x}(\frac{\partial u}{\partial x}i)+\frac{\partial}{\partial y}(\frac{\partial u}{\partial y}j))+q(x,y)u(x,y)=f(x,y)$