How to specify boundary conditions for solution of ODes

Hi everyone,

How can I specify boundary conditions in a matrix to solve the ODE system with the following dsolve command syntax?

syms x1(t) x2(t).....xN(t)

A = [a1 a2....aN; b1 b2...bN;...;d1 d2....dN];

B = [t1; t2;...;tN];

Y = [x1; x2;...;xN];

S = dsolve(diff(Y) == A*Y + B);

Answer 1

[Mischa Kim]

saheed, see e.g.

 syms R L C Uc(t) 

 % Define first and second derivatives for Uc
 DUcDt   = diff(Uc);
 D2UcDt2 = diff(Uc,2);

 % Perturbation input (or RHS): change input to dirac(t), t, etc.
 Uin     = 1;

 % Define differential equation for linear RLC circuit
 RLC_DE  = L*C*D2UcDt2 + R*C*DUcDt + Uc == Uin;

 % Set initial conditions
 Uc0     = Uc(0)    == 0;
 DUc0    = DUcDt(0) == 0;

 % Solve differential equation and display
 Uc_sym  = dsolve(RLC_DE, Uc0, DUc0);
 display(['Uc(t) = ',char(10),char(Uc_sym),char(10)])

Alternatively, check out this example in the documentation.

[saheed]

Thanks Kim but actually I have tried this syntax you specified but I got error because I need to specify the differential terms A, Y and B in

S = dsolve(diff(Y) == A*Y + B);

as matrices and vectors respectively. So the problem still remains if I specify the conditions of [x1; x2;...;xN] in

Y = [x1; x2;...;xN];

as x1(0)==0, x2(0)==0

just like you suggested. Any further suggestion is highly welcomed.