System of Non-Linear ODE

Question

Does anyone have any clue of how to find an analytical solution for the following system:

$$ \frac{dF_1}{dt}=(p+qF_1-rF_2)(1-F_1) $$ $$ \frac{dF_2}{dt}=vF_1(1-F_2) $$

$p$, $q$, $r$ and $v$ are constants. $F_1(0)=F_2(0)=0$.

Answer 1

here is my attempt at a solution: split the system of two equations with the eqaution for $F_1$ decoupled from $F_2$ as $$\frac{dF_1}{dt} = \frac{1-F_1}{F_1}\mbox{ and }\frac{dF_2}{dt} = \frac{\nu(1-F_2)}{p+qF_1 - rF_2}.$$

we can solve $-F_1 + \ln(1-F_1) = t$ for $F_1.$ too bad no explicit solution for $F_1.$

i will see if can go any farther with this.