First Order ODEs

• Separation of Variables
• Exact and Inexact Equations → integrating factor
• Connection of Exact Equations, Integrating Factors, and Sturm Liouville Theorem

Nth Order ODEs

Nth Order ODEs

Second Order

$$ y''(x)+a_1(x)y'+a_2(x)y=F(x) $$

• Reduction of Order: By finding one solution $y_1(x)$ to our homogenous 2nd order ODE, by substitution $y(x)=u(x)y_1(x)$ we will obtain our general solution.

Nonhomogenous ODEs

Other methods:

Laplace Transform

Dirac-Delta Function

Systems of ODEs

System of N First Order ODEs

Nonlinear Systems of ODES

Non Linear Systems of ODEs