Page 272 - Schaum's Outline of Differential Equations

CHAP. 26] SOLUTIONS BY MATRIX METHODS 255

since the former equation involves one less matrix multiplication. However, the integrals arising in (26.3) are
generally more difficult to evaluate than those in (26.2).

SOLUTION WITH NO INITIAL CONDITIONS

If no initial conditions are prescribed, the solution of x(?) = Ax(?) + f (?) is

or, when f(t) = 0,

where k is an arbitrary constant vector. All constants of integration can be disregarded when computing the
integral in Eq. (26.5), since they are already included in k.

Solved Problems

26.1. Solve x + 2x-Sx = 0;x(l) = 2, i(l)=3.
From Problem 17.2, this initial-value problem is equivalent to Eq. (26.1) with

A(
The solution to this system is given by Eq. (26.4). For this A, e is given in Problem 16.2; hence,

Therefore,

and the solution to the original initial-value problem is