I need to resolve this system of equation
v1[x_]''''=q/B
v2[x_]''''+t2^2*v2[x_]''=0
v3[x_]''''+t3^2*v3[x_]''=0
then:
v1[x_] := A1 + B1*x + C1*x^2 + D1*x^3 + q*x^4/(24*B)
v2[x_] := A2 + B2*x + C2*Cos[t2*x] + D2*Sin[t2*x]
v3[x_] := A3 + B3*x + C3*Cos[t3*x] + D3*Sin[t3*x]
with B>0 and p2 and p3 are in function of q
t2 = Sqrt[p2/B]
t3 = Sqrt[p3/B]
I have 14 boundary condition
eq1 := v1[0] == 0
eq2 := v1''[0] == 0
eq3 := v3[0] == 0
eq4 := v3''[0] == 0
eq5 := v2'[l/2] == 0
eq6 := - v2'''[l/2] - t2^2 v2'[l/2] == 0
eq7 := v1'[l/2] - v3'[l] == 0
eq8 := v2'[0] - v3'[l] == 0
eq9 := - v1''[l/2] + v2''[0] - v3''[l] == 0
eq10 := v1[l/2] == 0
eq11 := v2[0] == 0
eq12 := v3[l] == 0
eq13 := -t2^2 - (- v3'''[l] - t3^2 v3'[l]) == 0
eq14 := -v1'''[l/2] - (-v2'''[0] - t2^2 v2'[0]) + t3^2 == 0
for the 14 unknowns constant (A1,B1,C1,D1,A2,B2,C2,D2,A3,B3,C3,D3,p2,p3). I need to resolve the nonlinear system, find p2 and p3, put them into the system to find q by doing the determinant of the matrix of coefficient=0.
my problem is that i don't know how to resolve the nonlinear system