# 2: Higher order linear ODEs

- Page ID
- 32179

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We have already studied the basics of differential equations, including separable first-order equations. In this chapter, we go a little further and look at second-order equations, which are equations containing second derivatives of the dependent variable. The solution methods we examine are different from those discussed earlier, and the solutions tend to involve trigonometric functions as well as exponential functions. Here we concentrate primarily on second-order equations with constant coefficients.

- 2.3: Higher order linear ODEs
- The basic results about linear ODEs of higher order are essentially the same as for second order equations, with 2 replaced by nn . The important concept of linear independence is somewhat more complicated when more than two functions are involved.

- 2.4: Mechanical Vibrations
- Let us look at some applications of linear second order constant coefficient equations.

- 2.5: Nonhomogeneous Equations
- What about nonhomogeneous linear ODEs? For example, the equations for forced mechanical vibrations.

- 2.6: Forced Oscillations and Resonance
- Let us consider to the example of a mass on a spring. We now examine the case of forced oscillations, which we did not yet handle.

- 2.E: Higher order linear ODEs (Exercises)
- These are homework exercises to accompany Libl's "Differential Equations for Engineering" Textmap. This is a textbook targeted for a one semester first course on differential equations, aimed at engineering students. Prerequisite for the course is the basic calculus sequence.