ABSTRACT
Second-order linear equations are important because they arise frequently in engineering and physics. For instance, acceleration is given by the second derivative, and force is mass times acceleration. This chapter discusses second-order linear equations with constant coefficients. The “constant coefficient” attribute means that the coefficients in the equation are not functions: they are constants. “Undetermined coefficients” is a method of organized guessing. The chapter shows the technique can be expanded to cover inhomogeneous second-order linear equations. Variation of parameters is a method for producing a particular solution to an inhomogeneous equation by exploiting the solutions to the associated homogeneous equation. When a physical system in stable equilibrium is disturbed, then it is subject to forces that tend to restore the equilibrium. The result can lead to oscillations or vibrations, and is described by an ordinary differential equation.
