Advanced Engineering Mathematics, 7th Edition

10. 4 Nonhomogeneous Linear Systems

INTRODUCTION

The methods of undetermined coefficients and variation of parameters used in Chapter 3 to find particular solutions of nonhomogeneous linear ODEs can both be adapted to the solution of nonhomogeneous linear systems. Of the two methods, variation of parameters is the more powerful technique. However, there are instances when the method of undetermined coefficients provides a quick means of finding a particular solution.

In Section 10.1, we saw that the general solution of a nonhomogeneous linear system X′ = AX + F(t) on an interval I is X = X_c + X_p where X_c = c₁X₁ + c₂X₂ + + c_nX_n is the complementary ...