Solutions of Homogeneous Linear System of DE
where and are eigenvalue and eigenvector for respectively.
If and are two solutions to a homogeneous SDE , then is also a solution for any scalars , .
General Solutions (Complex Eigenvalues)
1) Let be an eigenvalue corresponding to eigenvector . (The eigenvectors are complex conjugates: .)
3) The general solution is
How to Sketch Phase Portrait
Probably the best video on how to sketch Phase Portrait: