Not sure what you're trying to achieve. You have Laplace's equation
It won't reduce to more than that.
Can anyone assist in solving the attached question?
I believe the PDE is ellipitic becasue B^2-AC = 0 -(1)(1)<0 implies elliptic.
Therefore we can write
Therefore I choose y-ix = Const. From this I choose new variables with s(x,y)= y and t(x,y)=-x
Not sure what to do after this
For part I, directly substitute into to show it is identically satisfied. For part ii, yes what you have done is correct except for the 2 in the denominator of the first one and those arbitrary functions must both be a constant (the same constant as we want the same answer).
Another way to do this is to consider
Then set giving, thus (if is real then ). So .
Thus simplify and the imaginery part is your .