**Solutions of Homogeneous Linear System of DE**

where and are eigenvalue and eigenvector for respectively.

**Superposition Principle**

If and are two solutions to a homogeneous SDE , then is also a solution for any scalars , .

**Euler’s formula**

**General Solutions (Complex Eigenvalues)**

1) Let be an eigenvalue corresponding to eigenvector . (The eigenvectors are complex conjugates: .)

2) Construct

3) The general solution is

## How to Sketch Phase Portrait

Probably the best video on how to sketch Phase Portrait: