12: Series Solutions of Linear Second Order Equations — Read

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In this Chapter, we study a class of second order differential equations that occur in many applications, but cannot be solved in closed form in terms of elementary functions.

12.1: Prelude to Series Solutions of Linear Second Order Equations
Second order differential equations occur in many applications, but cannot be solved in closed form in terms of elementary functions including Bessel's, Airy's and Langendre's Equations that can be written in the form P0(x)y′′+P1(x)y′+P2(x)y=0. These equations do not, in general, have closed form solutions, we seek series representations for solutions.
12.2: Review of Power Series
Many applications give rise to differential equations with solutions that can’t be expressed in terms of elementary functions such as polynomials, rational functions, exponential and logarithmic functions, and trigonometric functions. The solutions of some of the most important of these equations can be expressed in terms of power series. We’ll study such equations in this chapter. In this section we review relevant properties of power series.
- 12.2.1: Review of Power Series (Exercises)
12.3: Series Solutions Near an Ordinary Point I
Many physical applications give rise to second order homogeneous linear differential equations of the form P₀(x)y″+P₁(x)y′+P₂(x)y=0.
- 12.3.1: Series Solutions Near an Ordinary Point I (Exercises)

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