Solving a PDE to Yield Determining Equations I'm going through an example in Peter Hydon's book "Symmetry Methods for Differential Equations" which finds the basis for the Lie Algebra of the point symmetry generators for Burgers' equations. Burgers' equation is given in this case as:
$u_t+uu_x=u_{xx}$
So x and t are the independent variables. One part of the linearised symmetry condition is given as:
$2\xi_x+2\xi_uu_x-\tau_t=0$
The book continues to state $\xi_u=0$ - how does one show this exactly? Using information given later on I can reason this but for the life of my I can't figure out how to take the above line and show that $\xi_u=0$. I know from earlier working that $\tau=\tau(t)$ but as far as I can tell I shouldn't know at this point what $\xi$ is a function of so that doesn't really help me much to show $\xi_u=0$ right? Also I understand that from Burger's equation I know that $u_x\neq0$ or else the solution would be trivial, so just need to figure out how to show that term is equal to 0.
Thank you!

Ok, the answer is quite simple, I simplified the question too much. The book actually states the equations as:
$(\eta_u-\tau_t)u_t-\xi_u u_x u_t = (\eta_u - 2\xi_x - 3\xi_u u_x )u_t $
As can be seen the results they got were simply obtained by equating terms with the same coefficients $u$ of a particular derivative. By removing them I was unable to solve it. Had a feeling was something silly. :P
