newbie: solving system of 1st order ODEs with desolve

Dear Members,

I'm a newbie at Maxima, and although I enjoy using it, I'm stuck with a
problem. I'm trying to solve a system of 1st order ODEs with desolve:

eqn_1: 'diff(L(t),t)=(bL*dM*N(t)-mL*L(t))*(1-L(t)/K)-bM*L(t);
eqn_2: 'diff(N(t),t)=bM*L(t)-dM*mM*N(t)-(1-dM)*mdM*N(t);

Using

atsolve(L(t),t=0,0);
atsolve(N(t),t=0,1);

desolve([eqn_1,eqn_2],[L(t),N(t)]);

I get a solution that has laplace and ilt terms in it, and I don't know how
to expand/remove these terms. I attempted to follow the Example at
http://maxima.sourceforge.net/docs/tutorial/en/gaertner-tutorial-revision/Pages/ODE0002.htmon
solving a system of first order ODEs by Laplace transforming the
equations, solving for the laplace transforms with linsolve, and then
inverse laplace transforming those solutions. However, the solutions ended
up having a number of different laplace terms left in them again. I suspect
that the issue might be that these equations are non-linear, because I
noticed that the solution of linsolve for the laplace transforms has other
laplace terms in it as well. Therefore, I tried to look at the contrib_ode
package, but I didn't find a way to run it with a system of two equations.

Is there a better way to arrive at a closed form solution for L(t) and N(t)?


All suggestions are greatly appreciated.

-- 
Krisztian Magori

postdoctoral researcher
Drake Lab
Odum School of Ecology
University of Georgia

www.twitter.com/BiteOfAMosquito