dx/dt = A(t)x+f(t).
The associated initial value problem (IVP) is the system above plus the initial conditions x(t0)=x0
x = c1 x1(t) + c2x2(t) + ... + cnxn(t)
Using the fundamental matrix X(t)=[x1(t) ... xn(t)], the general solution is x(t) = X(t)c. Here, the vector c is an n x 1 column of constants, the ck's. To solve the IVP, determine the scalars via
c=X(t0)-1x0
x1(t)=eatcos(bt)v -
eatsin(bt)w
x2(t)=eatsin(bt)v +
eatcos(bt)w.
poly, roots, eig
inv, det
residue