Quadratic system of ODEs

Question

I have a quadratic ODE system that looks like this: $\dot{x}=Ax+diag(x)Nx$ where $x \in R^n$ and $A,N \in R^{n \times n}$ and $diag(x) \in R^{n \times n}$ is a diagonal matrix in which $x$ is its main diagonal. Is there a known solution to this system? Any hints, articles, papers or books about this kind of systems would be appreciated. Thanks.