December 2020
Intermediate to advanced
1064 pages
49h 13m
English
Content preview from Advanced Engineering Mathematics, 7th Edition
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3.4 Undetermined Coefficients
INTRODUCTION
To solve a nonhomogeneous linear differential equation
any(n) + an−1y(n−1) + … + a1y′ + a0y = g(x) (1)
we must do two things: (i) find the complementary function yc; and (ii) find any particular solution yp of the nonhomogeneous equation. Then, as discussed in Section 3.1, the general solution of (1) on an interval I is y = yc + yp.
The complementary function yc is the general solution of the associated homogeneous DE of (1), that is,
any(n) + an−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 ...
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