The differential transformation method is essentially a power series solution (some authors appear to think that it is actually a Taylor series method in disguise?!). It would seem to be appropriate for an initial-value problem, where the expansion point of the power series is the initial vaue.
For a BVP with defined at two (boundary) points, about whihc of these points would the power series expansion take place? Hence the DTM would seem to be completely inappropriate for general BVPs.
For your example, a DTM method appears not only inappropriate, but unnecessary. One only has to decide how to handle the boundary condition at" infinity". The conventional approach is to choose the value of the second boundary to be a "large" number, (eg try 10, 100, 1000) as a substitute for "infinity" and see if the solution appears to settle down to something "reasonable".
The attached code appears to work for most values of the parameter delta and doesn't change form much if one sets the upper limit to 10,100,1000. The selected options in the dsolve() command were necessary to ensure a solution for the variious values of 'delta' and the selected upper limit