Question: Strange and unuseful solution to ODEs

Hi everyone,

I am trying to solve a coupled ODE with variables c(T) and p__c(T) and these equations have a quantum parameter in them called beta__c which is a constant. The solutions to both p__c and c should naturally have beta__c in them, but in Maple they don't (in p__c particularly), while in Mathematica they do (beta2 in Mathematica is the same as beta__c in Maple). This is extremely important since we don't have the boundary conditions to fix the constants of integration of the solutions to p__c and c from ODEs, but we can use the the classical limit, beta__c -->0, of the ODE solutions we obtained, to match the classical solutions and ODE solutions, to fix the integration constants c1 and c2.

Below I am attaching the solutions of Maple and Mathematica. Can you advise how can I get solutions similar to Mathematica that have beta__c in them (particularly in p__c) such that one can actually take the  limit beta__c -->0 ?
In the Mathematica file beta2 is the same as beta__c in Maple.

Here is the Maple solution:

and here is the Mathematica solution which clearly has beta1 in both pc and c and also one can take the limit beta1-->0:


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