Integrability and linearizability of symmetric three-dimensional quadratic systems

We study local integrability and linearizability of polynomial and analytic systems of ODEs. It is proven that in the case of non-degenerate singularity if an analytic system is completely integrable and one equation is linearizable, then the system is linearizable in a neighborhood of the singularity. Some integrable and linearizable systems in a family of three-dimensional quadratic autonomous systems of ODEs depending on ten parameters are found.