Recent content by meatpuppet

I think I need to take a book out from the library and refresh myself on PDEs etc. As far as S being a rotation matrix, that makes sense, as the equation is the second derivative of the field in the direction which is omega degrees from the y-axis in the x-y plane. The motivation is that I...

Ok, so in my system: \sin^2 \omega u_{xx} + 2 \sin \omega \cos \omega u_{xy} + \cos^2 \omega u_{yy} = D This gives: M = \left[ \begin{array}{c c} \sin^2\omega & \sin\omega\cos\omega\\ \sin\omega\cos\omega & \cos^2\omega\end{array}\right] which has: S = \left[ \begin{array}{c c} -\cot\omega...

I follow everything up to this point, S in my case being S=\left[ \begin{array}{c c} -\cot\omega & \tan\omega\\ 1 & 1\end{array}\right] However thereafter I'm lost. Or rather I don't understand how to apply the knowledge of S to the system to be able in the end to derive u_{xy} (or u_{yy}.

Given the available conditions, assuming the solution: u = c_1 + c_2x + c_3y + c_4xy + c_5x^2 + c_6y^2 It is not possible to find either c_4 or c_6

I've tried and failed to search for this on the forum, so apologies if this has been answered many times before. Given a variable u which is a function of x and y: u = u\left(x,y\right)\\ is it possible to solve the pde: Au_{xx} + 2Bu_{xy} + Cu_{yy} = D\\ The knowns are: The real...