I would like to solve the following differential equation system,
$$ \frac{dx}{dt} = C_{1}\cdot x(t) + C_{2}\cdot x(t)^{2} +C_{3}\cdot x(t)\cdot y(t)\\ \frac{dy}{dt} = C_{4}\cdot y(t) + C_{5}\cdot y(t)^{2} +C_{6}\cdot x(t)\cdot y(t)$$
where $$C_{1},C_{2},C_{3},C_{4},C_{5},C_{6} $$ are constants and the initial conditions are given, $$ x(t=0) = xt_{0}\qquad y(t=0) = yt_{0}$$ and the values of the variables in equilibrium when $$ \frac{dx}{dt} = 0 \qquad \frac{dy}{dt} = 0 $$ are also given: $$ x_{0} = 0 \qquad y_{0} = 0$$
Could someone give me any advise or method to help me find the analytic solution of x(t), y(t).
Thanks in advance.