I found a way to do this, but I will need to wait until I get to my desktop to write through all of the steps as simplify() gave some unexpected results that are not understandable as-is.
The approach is to notice that the last sub-expression of the first two equations is the same as the expression for Dc. The first two are like Da=P+Dc , Db=-P+Dc in form. Select down to those two with the sub-expression replaced by Dc and dsolve. You will get solutions for a and c.
Take the expression for c and substitute t=0 to get c(0). You will get an expression in C1, C2, and some other terms and you know that c(0)=0 so solve() the expression for C2. The result will involve b(0) but we know that b(0)=0 so subs() that to get C2.
Now subs that C2 into the solution for a. subs t=0, solve() that equal 0.26 for C1, subs b(0)=0 and you get out C1
Now go back to the solutions for a and c and substitute in C1 and C2 and b(0)=0 to get the final a and c. Do not simplify() c!!! -- you will get weird results if you do!
Those in hand, go back to the second equation giving the expression for Db and substitute a and c and derivative of c to get Db.
At this point I simplify() and the dB term disappeared, and it was then that I noticed unexpected functions in the output, which I traced back to my having simplify() after I subs C1 into c. So at the moment I do not have the final production for b, but it should be down to a single equation and b(0)=0 will clearly be important. This resolution will have to wait until I get to my desktop.
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