Question: How find thus parameter with subscript for testing in pdes?

i am in big truble about finding solution of pdes i solved more than 20 and more pdes equation  and i thought becuase the solution is  long pdetest is not give me answer but last night i let the pc give me answer and my pdetest  show me i am in mistake and my solution is not the true solution i start to search again and i figure out there is must be  a problem i have a lot pdes in front of me but i chose this one as clear version in case need more i will upload it here   

please help me for finding thus B_13 and B_23 i just can find B_12 and becuase i replace just B_12 in each of B_13,B_23 my pdes is not give me zero  i need find true eq(19) i will upload three diffrent file for each one in top  for pdes,B_12, and eq(19) which is eqf1 in file 

interaction.mw

eqf1.mw

B12.mw