Yes, certainly possible. The basic approach would be to turn it into a system of first order odes of twice the dimension as follows (where x and xdot are vectors):
y1 = x
y2 = xdot
then, if A is invertible
y1' = y2
y2' = A \ (-B*y2 - c*y1 + p(t))
You'd then write a file to implement this in MATLAB like this
function dy = myode(t, y)
n = numel(y)/2;
y1 = y(1:n);
y2 = y(n+1:2*n);
dy = [y2; A \ (-B*y2 - c*y1 + p(t))
end
and solve it with ode45 (or whichever solver happens to be most suitable) as usual.
