Part III Linear Constant Coefficient Methods
As we delve deeper into the world of differential equations, it’s time to expand our solution techniques beyond first-order equations. Higher-order linear differential equations, those involving second derivatives or higher, are fundamental in modeling more complex systems in physics, engineering, and other fields.
In this chapter, we will explore powerful methods for solving these equations, starting with the characteristic equation for linear homogeneous equations with constant coefficients. We’ll then move on to techniques like undetermined coefficients and variation of parameters, which provide us with tools to tackle non-homogeneous equations. By mastering these methods, you’ll gain a robust toolkit for solving a wide range of higher-order linear differential equations.
