I am learning how to use Maple for solving single and systems of linear PDE's using the Laplace transform (LT)method so the resulting solution in s space can be used to generate the moments of the resulting probability distribution.

When I take the LT of a term such as Uxx(t,x), I expect a second order ordinary derivative. Instead, it shows the Laplace transform operator.

Here is a simple test code  

with(inttrans):

with(DEtools):

rhs_pde := diff(u(x, t), x, x);

laplace_rhs_pde := laplace(rhs_pde, t, s);

The following differential equation occurs during blending of two fluid in a continuous flow stirred tank

I want to replace the quantities in parenthesis on the RHS with the following variables (so-called deviation variables) where the overbar variables are constants and x₁, x₂ and x are variables.

When I use the subs command or algsubs command, it doesn't perform the substitution.

What is the best way to perform this operation?