This chapter explores second-order differential equations, which are fundamental in physics and engineering for modeling many systems. The text defines the general form of these equations and focuses on linear varieties where solutions are typically derived by combining the general solution of a homogeneous equation with a particular solution of a non-homogeneous one. Key analytical techniques covered include using variable substitution to reduce the order of the equation and identifying exact equations that can be integrated directly. Furthermore, the chapter provides numerous solved examples—ranging from basic linear forms to more complex equations explicitly containing the dependent variable—and demonstrates how to verify these solutions manually and through MATLAB software