Hi all,
Working though this problem, I have reached a proof I am not sure of the method, any opinions much appreciated!
Q:
where ; then satisfies :
where
------ This part is fine with some partial differentiation, chain rule and substitution, I can get the proof.
2nd proof:
show that is independant of if
------ This proof is also fine with some partial differentiation and change of variable
ending with
3rd proof:
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)