DE-BOOK Homogeneous

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Chapter 6 Homogeneous

As you might expect, solving differential equations becomes more challenging as the order of the derivative increases. But don’t worry! There’s a class of higher-order equations that are not only approachable but also serve as a gateway to more advanced topics. These are known as linear homogeneous differential equations with constant coefficients, or LHCC for short.

In this chapter, we will learn how to identify LHCC equations and explore a method to solve them by connecting them to a polynomial equation, called the characteristic equation. By the end of this section, you’ll see how solving higher-order equations can be as simple as finding the roots of a polynomial.

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