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# MATH 204

BS Mathematics

4

6

30

30

0

## Content

#### 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.

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