How to solve ODEs with imaginary eigenvalues?



Hi,

I have a question on solving a system of ODEs, where the eigenvalues have
imaginary values.  If I remember my long-ago differential equations
class, this ought to mean there's a solution which (by Euler's formula?)
can be expressed in terms of sines and cosines.  So how do I get Maxima
to give me that?

Here's a concrete example.  It's an RLC circuit, with variable R as a
function of I and V.  So I get the equations from the problem statement as
 
    dI/dt = (-1/L) (I**3 + 4I + V)
    dV/dt = I/K

(Where I use K for capacitance instead of C, 'cause Maxima uses C for its
own purposes.)

I translate that into Maxima input, (with specified values of L & K), and solve,
thusly:

    L: 1$
    K: 1/5;
    
    f1 : (-I^3 - 4 * I - V) / L$
    f2 : I / K$
    
    A: matrix ([diff (f1, I), diff (f1, V)], [diff (f2, I), diff (f2, V)])$
    B: A, I:0, V:0$
    evec: eigenvectors (B);
    evals: eigenvalues (B);

Maxima gives me back

    [[-%I - 2, %I -2], [1, 1]]

for the eigenvalues.  Now where do I go from here?  Is there a Maxima
command to give the solutions, or am I completely off track?

Thanks,
James