Clear["Global`*"]
b = Sqrt[L^2 - a^2];
p = Sqrt[L^2 - t^2];
w1 = A1*Sin[a*x]*Sin[b*y] + A2*Sin[a*x]*Cos[b*y] +
A3*Cos[a*x]*Sin[b*y] + A4*Cos[a*x]*Cos[b*y] +
A5*Sinh[t*x]*Sinh[p*y] + A6*Sinh[t*x]*Cosh[p*y] +
A7*Cosh[t*x]*Sinh[p*y] + A8*Cosh[t*x]*Cosh[p*y]
eq1 = (w1 /. x -> 0)
eq2 = ((D[w1, {x, 2}]) /. x -> 0)
eq3 = (w1 /. x -> 1)
eq4 = ((D[w1, {x, 2}]) /. x -> 1)
eq5 = (w1 /. y -> 0)
eq6 = ((D[w1, {y, 2}]) /. y -> 0)
eq7 = (w1 /. y -> 1)
eq8 = ((D[w1, {y, 2}]) /. y -> 1)
R = Normal@
CoefficientArrays[{eq1, eq2, eq3, eq4, eq5, eq6, eq7, eq8}, {A1, A2,
A3, A4, A5, A6, A7, A8}][[2]]
MatrixForm[R]
Det[R];
MatrixRank[R]
Inverse[R]
NullSpace[R]
I have an equation I am trying to apply boundary conditions to that equation. I have eight unknown coefficients in that equation and I have eight equation, now I am expressing it in matrix form Ax=0 and trying to solve the NUll space of that.But the problem is the matrix contains terms which are having a dependency on x and y. How to deal with this situation. My professor solved this manually in the class by eliminating terms after applying boundary conditions.But the result I am getting is different from the one mentioned in the reference book.
