Advanced Engineering Mathematics, 7th Edition

3.4 Undetermined Coefficients

INTRODUCTION

To solve a nonhomogeneous linear differential equation

a_ny⁽ⁿ⁾ + a_n−1y⁽ⁿ⁻¹⁾ + … + a₁y′ + a₀y = g(x) (1)

we must do two things: (i) find the complementary function y_c; and (ii) find any particular solution y_p of the nonhomogeneous equation. Then, as discussed in Section 3.1, the general solution of (1) on an interval I is y = y_c + y_p.

The complementary function y_c is the general solution of the associated homogeneous DE of (1), that is,

a_ny⁽ⁿ⁾ + a_n−1y⁽ⁿ⁻¹⁾ + … + a₁y′ + a₀y = 0.

In the last section we saw how to solve these kinds of equations when the coefficients were constants. Our goal then in the present section is to examine a method for obtaining particular solutions.

Method of Undetermined Coefficients ...