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Writing Laplace boundary condition in Wolfram Language

Posted 1 month ago

I would like to know how to convert the following image into Mathematica. I attempted to do so with the following code:

enter image description here

(* Step 1: Define the boundary condition PDE (S-6) *)
bc1PDE = (Vc/(Z*Rg*T)) D[pc[t], t] == diff * A * (D[c[z, t], z]);

(*bc1PDEf[y_] := (Vc/(Z*Rg*T)) D[pc[t], t] == diff * A * (D[c[z, t], z] /. z -> y);*)
(* Step 2: Apply the Laplace Transform to the boundary condition *)
boundaryConditionS6 = LaplaceTransform[bc1PDE, t, s];

(* Step 3: Dividing Both sides by A*)
eqManipulated = DivideSides[boundaryConditionS6, A];

(* Step 4: Assuming A != 0 *)
eqManipulated = Simplify[eqManipulated, A != 0];


(* Step 5: Substitute Vc/A with h *) (*Where h = Vc/A*)
boundaryConditionS6 = eqManipulated /. (Vc/A) -> h;

(* Step 6: Display in TraditionalForm *)
boundaryConditionS6 // TraditionalForm

But it gave me this error:

enter image description here

Any advice?

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