I have a linear equation that comes as a result of applying orthogonality on a non-homogeneous boundary condition with two unknowns $C_1$ and $C_2$. Can someone help me to express this equation in the form:
$$a(C_1) + b(C_2)=c\tag A$$
The code to derive the equation is as follows:
T[x_, y_, z_] = (C1* E^(γ z) + C2* E^(-γ z))*Sin[(α x/L) + β]*Sin[(δ y/l) + θ] + Ta;
tc[x_, y_] = E^(-bcy/l)*{tci + (bc/l)*Integrate[E^(bc*s/l)*T[x, s, 0], {s, 0, y}]};
bc1 = (D[T[x, y, z], z] /. z -> 0) == pc (T[x, y, 0] - tc[x, y]);
ortheq1 = Integrate[(bc1[[1]] - bc1[[2]])*Sin[(α x/L) + β]*Sin[(δ y/l) + θ], {x, 0, L}, {y, 0, l}, Assumptions -> {C1 > 0, C2 > 0, L > 0, l > 0, α > 0, β > 0, γ > 0, δ > 0, θ > 0, NTUC > 0, pc > 0, Ta > 0, tci > 0}] == 0;
One can also use the following to derive ortheq1
but it gives a longer result
ortheq1 = Integrate[bc1[[1]]*Sin[(α x/L) + β]*Sin[(δ y/l) + θ], {x, 0, L}, {y, 0, l}] == Integrate[bc1[[2]]*Sin[(α x/L) + β]*Sin[(δ y/l) + θ], {x, 0, L}, {y, 0, l}];
It is the ortheq1
that I would like in the form $(A)$.
C1
andC2
useCoefficientList
, else have a look atSelect
andFreeQ
. AlsoCollect[ortheq1, {C1, C2}]
might work. $\endgroup$List
({ }
) in the definition oftc
on purpose? $\endgroup$E^(-bcy/l)
. I should have used()
. $\endgroup$