# Phase portrait of homogeneous linear first-order system DE

## Description

Consider the homogeneous linear first-order system differential equations

*x*'=*ax*+*by*
*y*'=*cx*+*dy*

**'=***X***where***AX,***is the coefficients matrix. The following worksheet is designed to analyse the nature of the critical point (when ) and solutions of the linear system***A***'=***X**AX.***Notation:**- Determinant of
**A**: - Trace of
:**A** - Eigenvalues: ,
- Eigenvectors: ,

**Note:**The eigenvectors on the left-side screen are normalised.**Warning:**The online version does not show the case when there is only one eigenvector. You need to download the file.