Determining a Particular Solution for n-th Order Linear Differential Equations with Constant Coefficients

Determining a Particular Solution for N-th Order Linear Differential Equations with Constant Coefficients that Have the Free Term in the Following Form e a · x ·P(x) ·cos n x or e

“…In addition, for cases 1 and 3 we have to see if a is the solution of the equation 11. In these situations, we have 2 sub-cases: the sub-case in which a is not a solution of the equation (11) and the sub-case in which a is a solution of the equation 11, and in this sub-case we will assume that the multiplicity ordinal of the radical a is k. Under these conditions, as in [1], the particular solution of the equation 5is sought according to the rules established in that study, depending on the form of f (x) and the solutions of the equation 11. If f (x) is of the form (7) and a is not a solution of the equation 11, the particular solution of the equation (5) must be constructed as follows:…”