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A second order differential equation is a particular kind of differential equation in which the function's derivative is of order 2, and no further derivatives of the function are included in the equation. It contains terms that denote the function's second order derivative, such as y'', d2y/dx2, y''(x), etc. A second order differential equation is typically expressed as follows: y'' + p(x)y' + q(x)y = f(x), where p(x), q(x), and f(x) are functions of x. Using the auxiliary equation and other techniques, including the method of unknown coefficients and parameter modification, we may solve this differential equation. If the functions p(x) and q(x) are constants, the differential equation y'' + p(x)y' + q(x)y = 0 is referred to as a second-order differential equation with constant coefficients; if they are not, it is referred to as a second-order differential equation with variable coefficients. We shall examine these differential equations in-depth as well as their various varieties in this post. Along with learning alternative techniques, we will also learn how to determine the auxiliary equation and solve examples of second order differential equations with constant coefficients.