#### Objective

1. Know the different types of the differential equations.
2. Find the general and the particular solutions of a first order linear differential equation.
3. Find the general and the particular solutions of a second order linear differential equation with constant coefficients.
4. Find the general and the particular solutions of a second order linear differential equation with variable coefficients using the series.
5. Find the general and the particular solutions of a system of linear differential equations with constant coefficients using algebraic techniques.
6. Use the Laplace transform to transform a differential equation to another linear differential equation.

#### Content

A review on the differential equations of first order, Bernoulli equation, Riccati equation. Linear differential equations which can be solved by methods of order one.
Linear differential equations, WRONSKIEN. Differential equations with constant coefficients. Euler equations. Solutions of the form power series. Legendre Polynomial. Bessel equations. Bessel functions of the first and second kind.
Differential system. System with constant coefficients. Exponential of a matrix resolvent.
Laplace transform. Applications to solve an equation or a system.
Asymptotic behavior of a solution of a differential equation.