EQD-Review (TD2 - Ordinary Differential Equation and TD3 System of ODE)

Review:
TD2: Ordinary differential equation
1. First order ODE
1.1 Separable Variable
1.2 Separable Variable in form of y=ut
1.3 Linear Fraction
1.4 Exactness ODE
1.5 Standard Equation y'+p(t)y=q(t)
1.6 Bernulli's Equation y'+a(t)y = b(t)y^n
2. Second or Higher Order ODE
2.1 Homogeneous ODE a(t)y''+b(t)y'+c(t)y=0
2.2 Nonhomogeneous ODE a(t)y''+b(t)y'+c(t)y=f(t)
2.2.1 Using Underdetermined Coefficient Method
2.2.2 Using Differential Operator Method
2.2.3 Using Variational of Parameter Method
TD3: System of Ordinary Differential Equation
1. Homogeneous System of ODE in the form X'(t)=AX(t), A is square matrix.
1.1 Know how to calculate eigenvalues of matrix.
1.2 Know how to calculate eigenvector or eigenspace of matrix.
1.3 Know how to write the general solution of system of ODE.
1.4 Know to distinguish between different roots, repeat root, complex root of eigenvalues and find the eigenspace associated to those eigenvalues.
2. Nonhomogeneous System of ODE in the form X'(t)=AX(t)+B(t)
2.1 Calculate similarly to homogeneous System of ODE.
2.2 Recognize how to write particular solution X_p(t) based on B(t).