This program can compute the homomorphisms (includes gauge transformations) between
two differential operators, if such transformation exists.
It is part of newer versions of Maple, namely the Homomorphisms command
in the DEtools package.

Here is the help page (type ?DEtools[Homomorphisms] in Maple):

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DEtools[Homomorphisms] - compute the homomorphisms between two solution spaces

Calling Sequence
     Homomorphisms(L1, L2, domain)


Parameters
     L1     - differential operator

     L2     - differential operator

     domain - list containing two names


Description
- The input L1, L2 are differential operators. Denote V(L1) and V(L2) as the solution
  spaces of these two operators. If a map from V(L1) to V(L2) can be given in the form
  of a differential operator, then we call that map a homomorphism from V(L1) to V(L2).
  The command Homomorphisms computes a basis (as vector space) of all such
  homomorphisms, that is, it computes a basis of all operators r for which r(V(L1)) is a
  subset of V(L2). 

- In the special case L1=L2 the same can also be calculated with the command 
  DEtools[eigenring]. 

- Invertible homomorphisms (isomorphisms) from V(L1) to V(L2) are also called gauge
  transformations. If L1 and L2 belong to the same family of differential operators and
  differ only in their parameter values, then the name ladder operators is used as well.
  

- The argument domain describes the differential algebra. If this argument is the list 
  [Dt,t] then the differential operators are notated with the symbols Dt and t. They are
  viewed as elements of the differential algebra C(t)[Dt] where C is the field of
  constants, and Dt refers to the differentiation operator d/dt.

-  If the argument domain is omitted then the differential specified by the environment
  variable _Envdiffopdomain will be used. If this environment variable is not set, then
  the argument domain may not be omitted. 

- This function is part of the DEtools package, and so it can be used in the form 
  Homomorphisms(..) only after executing the command with(DEtools). However, it can
  always be accessed through the long form of the command by using 
  DEtools[Homomorphisms](..). 


Examples
> with(DEtools):

# Take the differential ring C(x)[Dx]: 
                                 
> _Envdiffopdomain := [Dx,x];

                              _Envdiffopdomain := [Dx, x]

> L1 := (x^2-x)*Dx^2+(a*x+b*x+x-c)*Dx+a*b;

                           2        2
                   L1 := (x  - x) Dx  + (a x + b x + x - c) Dx + a b

> L2 := subs(c = c+1, L1);

                         2        2
                 L2 := (x  - x) Dx  + (a x + b x + x - c - 1) Dx + a b

# Compute a basis for the homomorphisms r: V(L1) -> V(L2). 

> v := Homomorphisms(L1, L2);

                             v := [(x - 1) Dx - c + a + b]

# Since this basis has precisely one element, there is, up to multiplication by
# constants, precisely one map V(L1) -> V(L2) that can be presented by an operator r in
# C(x)[Dx].

# In the following example, every linear map V(L1) -> V(L2) can be presented by an
# operator. Thus, the dimension of all such maps will be order(L1)*order(L2) = 3*2 = 6.
# Since the output is a basis of these maps, it must have 6 elements. 

> L1 := Dx^3; L2 := Dx^2;

                                               3
                                       L1 := Dx

                                               2
                                       L2 := Dx

> Homomorphisms(L1, L2);

                       2      2        2   2                3   2      2
      [Dx, x Dx - 2, Dx , x Dx  - Dx, x  Dx  - 2 x Dx + 2, x  Dx  - 2 x  Dx + 2 x]


See Also 
DEtools[eigenring], diffop 


References
  [1] van der Put, M. and Singer, M. F. Galois Theory of Linear Differential Equations,
  Volume 328. Springer: 2003. An electronic version of this book is available at 
  http://www4.ncsu.edu/~singer/ms_papers.html.

  [2] van Hoeij, M. "Rational Solutions of the Mixed Differential Equation and its
  Application to Factorization of Differential Operators." ISSAC '96 Proceedings (1996):
  219-225.