Coupled nonlinear ODE equations system

Question

I am tying to solve the following coupled ODE equations system function of time:

\begin{equation} \left\{ \begin{aligned} & \dot{\alpha}(t) = p \ \alpha(t)^{2}+ q \ \alpha(t) + r \ \beta(t) + s \\ & \dot{\beta}(t) = u \ \beta(t) + v \ \alpha(t) \ \beta(t) + w \ \alpha(t) \end{aligned} \right. \end{equation}

$p, q, r, s, u, v$ and $ w$ are constants.

Any help?