Second Order Constant Coefficient Linear Differential Equations

Abstract

This chapter begins our study of second order linear differential equations, which are equations of the form

$$a(t)y\prime\prime + b(t)y\prime + c(t)y = f(t),$$

where a(t), b(t), c(t), called the coefficient functions, and f(t), known as the forcing function, are all defined on a common interval I. Equation (1) is frequently made into an initial value problem by imposing initial conditions: y(t ₀) = y ₀ and y′(t ₀) = y ₁, where t ₀ ∈ I.