Working though this problem, I have reached a proof I am not sure of the method, any opinions much appreciated!
where ; then satisfies :
------ This part is fine with some partial differentiation, chain rule and substitution, I can get the proof.
show that is independant of if
------ This proof is also fine with some partial differentiation and change of variable
further show when where is an arbitary constant....
Now given the second proof, is it possible to integrate the entire expression
where w r t : ?
reducing the orders of the differential terms? I suspect this is not possible since one of the terms contains a ..... if we cannot directly integrate to reduce the power, is it possible to use a power reduction? I suspect not since is an unknown function- not an explicit solution that allows this method..........
Thanks for reading!
(I realise the post is rather long winded, but I didnt want to miss info that the proof relied upon in previous sub part)