Question: parial derivative PDES

Dear all;

I have a function  C(S,t)  and I would like to show that this function is the solution of Partial differential equation ( denotes by PDES). I introduce all my function but when I try to simplify my PDES, I can not get zero as result. 

Many thanks for your help to simplify the PDES to get PDES=0. So, that C(S,t) is the solution of my PDEs.

simplification.mw

 

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