ABOUT ONE METHOD OF SOLVING NONHOMOGENEOUS LINEAR DIFFERENTIAL SECOND ORDER EQUATION WITH CONSTANT COEFFICIENTS
Keywords:differential equation, nonhomogeneous differential equation, characteristic equation, partial solution, general solution, method of undetermined coefficients, linear equation, linearly independent solutions.
The natural laws often are expressed as differential equations, and the calculation of these processes is reduced to solving differential equations. Linear differential equations of the second order with constant coefficients are one of the important
objects of investigation of the theory of ordinary differential equations. The paper proposes ways of constructing solutions of second-order linear differential equations with constant coefficients that differ from the classical construction method. The difference is that they do not use the concept of a complex number in the traditional presentation in the case of a negative discriminant of the characteristic equations of the corresponding linear differential equation with constant coefficients. In the case of a homogeneous differential equation, the essence of the proposed method lies in the construction of linearly independent
particular solutions of a linear second order equation by the application of the Bernoulli method to solve a linear first order equation