Comparsion of Solutions of Second Order Linear Differential Equations With Constant Coefficients

In this contribution we compare solutions of second order linear differential equations with constant coefficients with respect to the form of right-hand side of the equation and to the form of initial or boundary conditions. We will see that some types of such differential equations one can resolve by the method of variation of constants and it is not possible solve them by Laplace transform. On the other hand, some of them are solvable by Laplace transform and are unsolvable by the method of variation of constants. The reason for the comparison is to show that the students of automation have to know both ways of solving linear differential equations with constant coefficients.