In this problem you will use variation of parameters to solve the nonhomogeneous equation y′′+6y′+9y=−2e−3t
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The pair of linear equations has a unique solution. Then the pair of equations is consistent and independent.
<h3>What is the linear system?</h3>It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.
Given
are the linear equations.
We know the condition,
The pair of equations satisfies the condition.
The pair of linear equations has a unique solution.
If a system has at least one solution, the system is consistent.
If the consistent system has exactly one solution then the system is independent.
Thus, the pair of equations is consistent and independent.
More about the linear system link is given below.