Procedure for the techniques of undetermined coefficients

The general procedure in this technique is to assume the particular integral of a form similar to the right member in equation (1). The necessary derivatives of are then obtained and substituted into the given differential equation. This results in an identity for the independent variable, and consequently the coefficients of the like terms are equated. The values of the undetermined coefficients are found from the resulting system of linear equations. The procedure is best illustrated with an example

Table 1 below summarizes a general rule for the formulation of the particular integral

If is of the form	Choose to be

Table 1

Example 13: Find the particular integral of

Solution: Y ou actually worked out the complementary function of this equation to be . That is, the auxiliary equation is , giving or .Hence the complementary function is as before. Looking at the right hand side of the above differential equation example 13.3.1 and the general rule in table 1, the particular integral is

, ,

Substituting in the original equation

Comparing the coefficients on both sides

The general solution is then the complementary function + particular integral, which is

.

Поиск по сайту: