# 9: Linear Higher Order Differential Equations

- Page ID
- 9452

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

This chapter extend the results obtained in Chapter 5 for linear second order equations to linear higher order equations.

- 9.1: Introduction to Linear Higher Order Equations
- This section presents a theoretical introduction to linear higher order equations. We will sketch the general theory of linear n-th order equations.

- 9.2: Higher Order Constant Coefficient Homogeneous Equations
- In this section we consider the homogeneous constant coefficient equation of n-th order.

- 9.3: Undetermined Coefficients for Higher Order Equations
- This section presents the method of undetermined coefficients for higher order equations.

- 9.4: Variation of Parameters for Higher Order Equations
- This section extends the method of variation of parameters to higher order equations. We’ll show how to use the method of variation of parameters to find a particular solution of Ly=F, provided that we know a fundamental set of solutions of the homogeous equation: Ly=0.

*Thumbnail: The Wronskian. In general, for an n ^{th} order linear differential equation, if \((n-1)\) solutions are known, the last one can be determined by using the Wronskian.*