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