During a study, I have faced with the below nonlinear autonomous differential equation system, which is a bit similar to the Lotka-Volterra equations (but slightly different). \begin{equation}\left.\begin{array}{cc}\dot{x}=A\,y-B\,x\,y\\\dot{y}=C\,x-D\,x\,y\end{array}\right\},\quad\textrm{where}\qquad A,\,C>0\in\mathbb{R}\quad\textrm{and}\quad0<B,\,D<1\in\mathbb{R}\end{equation} Both $x$ and $y$ depend on time $t$. The $A,\,B,\,C,\,D$ coefficients are real constants. The initial conditions would be $x(0) = 0$ and $y(0) = 1$. I would like to have a real, exact analytical solution for this system, but I do not know how to get it.
I would like to ask of Your kind help with this problem. Thank you in advance.