Abstract
In this paper, we discuss how to build a local solution for a system of ordinary differentiable equations of quadratic forms by constructing a psi-series. We want to understand how the solution behaves around the singularities. There are a necessary and sufficient condition: Real leading coefficients ensure the occurrence of blow up in finite time, and real time singularity implies that the leading coefficients of one asymptotic series are real. The Psi-series of quadratic systems on the plane has been studied. The relationship between the behavior and integrability of the system is also illustrated.