It's very convenient to define a DE or PDE through Differential Operator D, for example,
((D[1, 1]+D[1, 2]+D[2, 2])(z))(x, y) = exp(x)*sin(y)
Is it possible to realize Inverse Operator Method of Operator D? How to solve the following equation if we rewrite the pde through inverse operator method?
(z)(x, y)=((D[1, 1]+D[1, 2]+D[2, 2])^(-1))exp(x)*sin(y)
Thanks a lot.