I have to solve the sistem of differential equation odesys with the condition imposed in bc vector. I obtain the "Invalid Initial Condition" at the line where v is defined, even if the domain for the boundary condition is correct. I must keep it a symbolic solution and a0 is a costant.

%% ANALYTICAL MODEL FOR A DCB SPECIMEN UNDER THE CONDITION OF PRESCRIBED DISPLACEMENTS
%% Linear Elastic Phase
%———
syms x d v0(x) v1(x) v2(x) Lcz
%———
phi0 = -diff(v0,x);
M0 = E*I*diff(v0,x,2);
T0 = E*I*diff(v0,x,3);
phi1 = -diff(v1,x);
M1 = E*I*diff(v1,x,2);
T1 = E*I*diff(v1,x,3);
phi2 = -diff(v2,x);
M2 = E*I*diff(v2,x,2);
T2 = E*I*diff(v2,x,3);
%———
ode_0 = diff(v0,x,4) == 0;
ode_1 = diff(v1,x,4) – 2*w*(lambda^2)*diff(v1,x,2) + (lambda^4)*v1 == 0;
ode_2 = diff(v2,x,4) + 2*ps*(k^2)*diff(v2,x,2) – k^4*(v2 – d_c/2) == 0;
%———
syms xL xR xI
xL = -a0 – Lcz;
xI = -Lcz;
xR = L – a0 – Lcz;
c1 = v0(xL) == d/2;
c2 = M0(xL) == 0;
c3 = v0(xI) == v2(xI);
c4 = phi0(xI) == phi2(xI);
c5 = M0(xI) == M2(xI);
c6 = T0(xI) == T2(xI);
c7 = v1(0) == v2(0);
c8 = phi1(0) == phi2(0);
c9 = M1(0) == M2(0);
c10 = T1(0) == T2(0);
c11 = v1(xR) == 0;
c12 = phi1(xR) == 0;
%———
odesys = [ode_0; ode_1; ode_2];
bc = [c1; c2; c3; c4; c5; c6; c7; c8; c9; c10; c11; c12];
v = dsolve(odesys, bc);
%———
v1_sol(x,d,Lcz) = simplify(v.v1);
v0_sol(x,d,Lcz) = simplify(v.v0);
v2_sol(x,d,Lcz) = simplify(v.v2);
phi0_sol(x,d,Lcz) = diff(v0_sol,x);
phi1_sol(x,d,Lcz) = diff(v1_sol,x);
phi2_sol(x,d,Lcz) = diff(v2_sol,x);
M0_sol(x,d,Lcz) = E*I*diff(v0_sol,x,2);
M1_sol(x,d,Lcz) = E*I*diff(v1_sol,x,2);
M2_sol(x,d,Lcz) = E*I*diff(v2_sol,x,2);
T0_sol(x,d,Lcz) = E*I*diff(v0_sol,x,3);
T1_sol(x,d,Lcz) = E*I*diff(v1_sol,x,3);
T2_sol(x,d,Lcz) = E*I*diff(v2_sol,x,3);
%———
d_lim = solve(v0_sol(0,d,0) == d_0/2,d);
% d_max = solve(v0_sol(0,d,0) == d_0/2,d);
% Lcz_max = solve(v2_sol(-Lcz,d_max,Lcz) – d_c/2 == 0, x,[0 50]);
[d_max, Lcz_max] = solve([v1_sol(0,d,Lcz) – d_0/2 == 0, v2_sol(-Lcz,d_max,Lcz) – d_c/2 == 0],[d,Lcz]);I have to solve the sistem of differential equation odesys with the condition imposed in bc vector. I obtain the "Invalid Initial Condition" at the line where v is defined, even if the domain for the boundary condition is correct. I must keep it a symbolic solution and a0 is a costant.

%% ANALYTICAL MODEL FOR A DCB SPECIMEN UNDER THE CONDITION OF PRESCRIBED DISPLACEMENTS
%% Linear Elastic Phase
%———
syms x d v0(x) v1(x) v2(x) Lcz
%———
phi0 = -diff(v0,x);
M0 = E*I*diff(v0,x,2);
T0 = E*I*diff(v0,x,3);
phi1 = -diff(v1,x);
M1 = E*I*diff(v1,x,2);
T1 = E*I*diff(v1,x,3);
phi2 = -diff(v2,x);
M2 = E*I*diff(v2,x,2);
T2 = E*I*diff(v2,x,3);
%———
ode_0 = diff(v0,x,4) == 0;
ode_1 = diff(v1,x,4) – 2*w*(lambda^2)*diff(v1,x,2) + (lambda^4)*v1 == 0;
ode_2 = diff(v2,x,4) + 2*ps*(k^2)*diff(v2,x,2) – k^4*(v2 – d_c/2) == 0;
%———
syms xL xR xI
xL = -a0 – Lcz;
xI = -Lcz;
xR = L – a0 – Lcz;
c1 = v0(xL) == d/2;
c2 = M0(xL) == 0;
c3 = v0(xI) == v2(xI);
c4 = phi0(xI) == phi2(xI);
c5 = M0(xI) == M2(xI);
c6 = T0(xI) == T2(xI);
c7 = v1(0) == v2(0);
c8 = phi1(0) == phi2(0);
c9 = M1(0) == M2(0);
c10 = T1(0) == T2(0);
c11 = v1(xR) == 0;
c12 = phi1(xR) == 0;
%———
odesys = [ode_0; ode_1; ode_2];
bc = [c1; c2; c3; c4; c5; c6; c7; c8; c9; c10; c11; c12];
v = dsolve(odesys, bc);
%———
v1_sol(x,d,Lcz) = simplify(v.v1);
v0_sol(x,d,Lcz) = simplify(v.v0);
v2_sol(x,d,Lcz) = simplify(v.v2);
phi0_sol(x,d,Lcz) = diff(v0_sol,x);
phi1_sol(x,d,Lcz) = diff(v1_sol,x);
phi2_sol(x,d,Lcz) = diff(v2_sol,x);
M0_sol(x,d,Lcz) = E*I*diff(v0_sol,x,2);
M1_sol(x,d,Lcz) = E*I*diff(v1_sol,x,2);
M2_sol(x,d,Lcz) = E*I*diff(v2_sol,x,2);
T0_sol(x,d,Lcz) = E*I*diff(v0_sol,x,3);
T1_sol(x,d,Lcz) = E*I*diff(v1_sol,x,3);
T2_sol(x,d,Lcz) = E*I*diff(v2_sol,x,3);
%———
d_lim = solve(v0_sol(0,d,0) == d_0/2,d);
% d_max = solve(v0_sol(0,d,0) == d_0/2,d);
% Lcz_max = solve(v2_sol(-Lcz,d_max,Lcz) – d_c/2 == 0, x,[0 50]);
[d_max, Lcz_max] = solve([v1_sol(0,d,Lcz) – d_0/2 == 0, v2_sol(-Lcz,d_max,Lcz) – d_c/2 == 0],[d,Lcz]); I have to solve the sistem of differential equation odesys with the condition imposed in bc vector. I obtain the "Invalid Initial Condition" at the line where v is defined, even if the domain for the boundary condition is correct. I must keep it a symbolic solution and a0 is a costant.

%% ANALYTICAL MODEL FOR A DCB SPECIMEN UNDER THE CONDITION OF PRESCRIBED DISPLACEMENTS
%% Linear Elastic Phase
%———
syms x d v0(x) v1(x) v2(x) Lcz
%———
phi0 = -diff(v0,x);
M0 = E*I*diff(v0,x,2);
T0 = E*I*diff(v0,x,3);
phi1 = -diff(v1,x);
M1 = E*I*diff(v1,x,2);
T1 = E*I*diff(v1,x,3);
phi2 = -diff(v2,x);
M2 = E*I*diff(v2,x,2);
T2 = E*I*diff(v2,x,3);
%———
ode_0 = diff(v0,x,4) == 0;
ode_1 = diff(v1,x,4) – 2*w*(lambda^2)*diff(v1,x,2) + (lambda^4)*v1 == 0;
ode_2 = diff(v2,x,4) + 2*ps*(k^2)*diff(v2,x,2) – k^4*(v2 – d_c/2) == 0;
%———
syms xL xR xI
xL = -a0 – Lcz;
xI = -Lcz;
xR = L – a0 – Lcz;
c1 = v0(xL) == d/2;
c2 = M0(xL) == 0;
c3 = v0(xI) == v2(xI);
c4 = phi0(xI) == phi2(xI);
c5 = M0(xI) == M2(xI);
c6 = T0(xI) == T2(xI);
c7 = v1(0) == v2(0);
c8 = phi1(0) == phi2(0);
c9 = M1(0) == M2(0);
c10 = T1(0) == T2(0);
c11 = v1(xR) == 0;
c12 = phi1(xR) == 0;
%———
odesys = [ode_0; ode_1; ode_2];
bc = [c1; c2; c3; c4; c5; c6; c7; c8; c9; c10; c11; c12];
v = dsolve(odesys, bc);
%———
v1_sol(x,d,Lcz) = simplify(v.v1);
v0_sol(x,d,Lcz) = simplify(v.v0);
v2_sol(x,d,Lcz) = simplify(v.v2);
phi0_sol(x,d,Lcz) = diff(v0_sol,x);
phi1_sol(x,d,Lcz) = diff(v1_sol,x);
phi2_sol(x,d,Lcz) = diff(v2_sol,x);
M0_sol(x,d,Lcz) = E*I*diff(v0_sol,x,2);
M1_sol(x,d,Lcz) = E*I*diff(v1_sol,x,2);
M2_sol(x,d,Lcz) = E*I*diff(v2_sol,x,2);
T0_sol(x,d,Lcz) = E*I*diff(v0_sol,x,3);
T1_sol(x,d,Lcz) = E*I*diff(v1_sol,x,3);
T2_sol(x,d,Lcz) = E*I*diff(v2_sol,x,3);
%———
d_lim = solve(v0_sol(0,d,0) == d_0/2,d);
% d_max = solve(v0_sol(0,d,0) == d_0/2,d);
% Lcz_max = solve(v2_sol(-Lcz,d_max,Lcz) – d_c/2 == 0, x,[0 50]);
[d_max, Lcz_max] = solve([v1_sol(0,d,Lcz) – d_0/2 == 0, v2_sol(-Lcz,d_max,Lcz) – d_c/2 == 0],[d,Lcz]); dsolve, ode, symbolic MATLAB Answers — New Questions

​