Variation of Parameters Method

In this section we consider a procedure for solving nonhomgeneous linear equation

[Maple Math] , where the functions [Maple Math] , and [Maple Math] are continuous. We will assume that we have already solved the homogeneous equation

[Maple Math] . In the case that the functions [Maple Math] and [Maple Math] are constants, in the previous section we saw how to find two linearly independent solutions [Maple Math] and [Maple Math] . The Method of Variations of Parameters works as follows. First, we solve the system [Maple Math] in [Maple Math] and [Maple Math] . (Here [Maple Math] stands for the derivative of a function [Maple Math] .) Next we find [Maple Math] and [Maple Math] by integrating [Maple Math] and [Maple Math] respectively#000000> respectively. Then a particular solution [Maple Math] is given by the formula [Maple Math] , and the general solution is

[Maple Math] .

Example 1: Solve [Maple Math] that satisfies initial conditions [Maple Math] and

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