This document discusses linear differential equations of second order with constant coefficients. It presents: 1) The general form of a second order linear differential equation with constant coefficients. 2) Methods for finding the complete solution, which is the combination of the complementary function (C.F.) and particular integral (P.I.). 3) Solutions for three cases of the auxiliary equation: when roots are real and distinct, real and equal, and imaginary. Worked examples are provided to illustrate each case.