In a forest, the fox population grows at a rate of 10% per year, and the wolf population at a rate of 25% per year. The species compete for the same resources, and the forest can support 10,000 foxes or 6,000 wolves (carrying capacities). By taking F(t) and W(t) to be the fox and wolf populations at any time t, formulate a mathematical model with a differential equation.
I have developed the model to be
$\frac{dF(t)}{dt}=0.1F(t)\left[1-\frac{F(t)}{10000}-\frac{aW(t)}{6000}\right]$
$\frac{dW(t)}{dt}=0.25W(t)\left[1-\frac{W(t)}{6000}-\frac{bF(t)}{10000}\right]$
Is it correct? Now, how do we solve these two differential equations?