The standard transposition is the involution of the Weyl algebra which sends xadb to (-d)bxa. It provides the equivalence in the Weyl algebra between left and right D-modules.
i1 : W = QQ[x,y,Dx,Dy, WeylAlgebra => {x=>Dx,y=>Dy}]
o1 = W
o1 : PolynomialRing
i2 : L = x^2*Dy + y*Dy^2 + 3*Dx^5*Dy
5 2 2
o2 = 3Dx Dy + x Dy + y*Dy
o2 : W
i3 : Dtransposition L
5 2 2
o3 = 3Dx Dy - x Dy + y*Dy + 2Dy
o3 : W
Caveat
The standard transposition of a left ideal should be a right ideal, however M2 currently doesn't support right modules. Thus the output is left ideal generated by the transposition of the previous generators.