Phase portrait of homogeneous linear first-order system DE


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: ,
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.