DSolve[{v1''''[z1]+fv1''[z1]+kv1[z1]-q0,v2''''[z2]+fv2''[z2]=q,v1[0]=q/k,v1'[0]=0,v1[a1]=v2[0],v1'[a]=v2'[0],v1''[a]=v2''[0],v1'''[a]=v2'''[0],v2''[a2]=0},{v1[z1],v2[z2]},{z1.z2}]
Set
:Tag Plus in f
′′
v2
[z2]+
(4)
v2
[z2] is Protected.
DSolve
:Equation or list of equations expected instead of q in the first argument -q+kv1[z1]+f
′′
v1
[z1]+
(4)
v1
[z1]0,q,
q
k
,0,v2[0],
′
v2
[0],
′′
v2
[0],
(3)
v2
[0],0.
DSolve-q+kv1[z1]+f
′′
v1
[z1]+
(4)
v1
[z1]0,q,
q
k
,0,v2[0],
′
v2
[0],
′′
v2
[0],
(3)
v2
[0],0,{v1[z1],v2[z2]},{z1.z2}