In[]:=
EOM=
∂
t,t
w[x,t]-2P
∂
x,x
w[x,t]+
∂
x,x,x,x
w[x,t]==-2ϵμ[x]
∂
t
w[x,t]+4ϵF
∂
x,x
w[x,t]Cos[Ωt]+ϵα
∂
x,x
w[x,t]
1
∫
0
2
(
∂
x
w[x,t])
x
and homogeneous boundary conditions
In[]:=
BC={w[0,t]==0,
∂
x,x
w[x,t]==0/.x->0,w[1,t]==0,
∂
x
w[x,t]==0/.x->1}