ODEs: Solving, critical points, phase portraits, solving for phase curves

Classify critical points

Find discriminant and eigenvalues using trace and determinant

Convert second order ODE to system of coupled first order ODEs

Sketching phase portraits

Solving systems of coupled linear ODEs

Sketching and solving for phase curves of non-linear systems

Solving inhomogeneous linear systems (RHS just constant vector)

Double angle formulas

Product to sum trig identities

Techniques for sketching phase portraits

Euler’s formula for converting complex solution to real form