# Apply IC and BCs on Second - Order Linear PDE

I am now trying to solve second - order linear partial differential equation in that interested eq. has been separated into variables to simplify the procedure for Mathematica. Here is my equation;

or separated form,

Also, the last equation is coded in Mathematica as;

    L[t_, z_] := T[t] Z[z]
Eq = (D[T[t], t]/(A*T[t])) == R*(D[D[Z[z], z], z]/Z[z]) - B*(D[Z[z], z]/Z[z])
L[t, z] /. Flatten@{DSolve[Eq[[1]] == F, T, t, GeneratedParameters -> CT],
DSolve[Eq[[2]] == F, Z, z, GeneratedParameters -> CS]}


Then, the solution is given as;

However at that point, I should plug IC and BCs into related eq. to both get rid of constants and proceed with my calculations. These are my IC and BCs, respectively;

How can I solve this problem? Is there any way to insert these IC and BCs into the code above? or Does there exist any method, command etc. to come up with solution without integration constants?

Note: Any of the values included in BCs is neither a function of z nor that of t.

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Enter your IC and BCs at the same time as your eqn, i.e. as a list of eqns. There are many examples in the documentation for DSolve. But of course you need to transform your IC and BCs in the same way that you transformed the eqn. Try doing that and then let us know if you have problems. –  Mike Honeychurch Jul 16 at 22:04