Find the eigenvalues for 3 equations after variable separation

I have to find the eigenvalues for three functions obtained with variable separation method.
The functions result from the following expression:

I tried with the following code:

W = 1.2;
Subscript[L, 1] = 0.5;
Subscript[L, 2] = 5;
Subscript[k, CLS] = 1.4;
Subscript[k, soil] = 2.2;
h = 2.5;

For Y:

eqy = Y''[y] + [Beta]^2*Y[y] == 0;
icy1 = Y'[y] == 0 /. y -> 0;
icy2 = Y'[y] == 0 /. y -> W;
soly = DSolve[{eqy, icy1, icy2}, Y[y], {y, 0, W}]
eigfuns = Table[Y[y] /. sol[[1]] //. {[FormalN] -> i, [Beta] -> 5.235987755982989` [FormalN]} /. {C[1] -> 1}, {i, 2}]

I don’t understand why the result for Beta is double the solution I should obtain.
As for X:

eqx1 = Subscript[X, 1]''[x] + Subscript[[Gamma], 1]^2*Subscript[X, 1][x] == 0;
eqx2 = Subscript[X, 2]''[x] + Subscript[[Gamma], 2]^2*Subscript[X, 2][x] == 0;
icx1 = -Subscript[k, CLS]*Subscript[X, 1]'[x] + h*Subscript[X, 1][x] == 0 /. x -> 0;
icx2 = Subscript[X, 2][x] == 0 /. x -> Subscript[L, 2];
ccx1 = Subscript[X, 1][x] == Subscript[X, 2][x] /. x -> Subscript[L, 1];
ccx2 = Subscript[k, CLS]*Subscript[X, 1]'[x] == Subscript[k, soil]*Subscript[X, 2]'[x] /. x -> Subscript[L, 1];
solx = DSolve[{eqx1, eqx2, icx1, icx2, ccx1, ccx2}, Subscript[X, 1][x], Subscript[X, 2][x], {x, 0, Subscript[L, 2]}]

In this case, it says that "DSolve::litarg: To avoid possible ambiguity, the arguments of the dependent variable in Subscript[X, 1][x] should literally match the independent variables.".
Finally for Gamma:

eqt = [CapitalGamma]'[t] + [Lambda]^2*[CapitalGamma][t] == 0;
ict1 = [CapitalGamma][t] == 25 /. t -> 0;
solt = DSolve[{eqt, ict1}, [CapitalGamma][t], {t, 0, 1000}]

I don’t think I have enough conditions to find lambda.
Can you check if I used to proper BC and give me some suggestions to solve the problems?
Thank you in advance!