Using Laplace transformation for a system of differential equations

Question

I need to solve a system of differential equations, but unfortunatelly my methods are very limited in this field. My system of differential equations is: \begin{align*} n'(t) &= -A·n(t) - a·n(t)·(N_{t}-N(t)) + b·N(t)·(n_{c}-n(t))\\ N'(t) &= -a·n(t)·(N_{t}-N(t)) - b·N(t)·(n_{c} - n(t)) \end{align*} where the contants: $a,b,n_{c},N_{t},A>0$ and $N\leq N_{t}$. The initial conditions: \begin{align*} n(t=0) &= n_{i}\\ N(t=0) &= N_{i} \end{align*}

I have tried to solve it straight forward with Maple:

eq1 := diff(n(t), t) = -A*n(t) - a*n(t)*(N_t - N(t)) + b*(n_c - n(t))*N(t);
eq2 := diff(N(t), t) = -a*n(t)*(N_t - N(t)) - b*(n_c - n(t))*N(t);
ics := n(0) = n_i, N(0) = N_i;
system_eqs := eq1, eq2;
Solution := dsolve({system_eqs,ics})

but i got a ´NULL´ Solution:

Solution := NULL

I have also tried it with Laplace method.

Solution_Laplace := dsolve({ics, sys_case_2}, {N(t), n(t)}, method = laplace);

Error, (in dsolve/inttrans/solveit) transform method can only be applied to linear ODE

From the error raised, I guess that the trouble applying the Laplace transform yields in the: $n(t)N(t)$ terms in my system, that makes it non-linear.

Does anyone know if it is possible to solve this system? OR any method/hint that i can start with?

Thanks in advance.