Let be the square matrix of order
. Suppose that
are linearly independent solutions of
. Then
SOLUTION
. Thus the eigenvalues are
. The eigenvector corresponds to
is obtained by
. Then the eigenvector is
. Thus
is a solution. The eigenvector corresponds to
is obtained by
. Thus the eigenvector is
. Therefore,
is a solution. Then the fundamental matrix is
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Let . Then
and the given differential equation
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(3.1) |
SOLUTION Using Cramer's rule, we have
SOLUTION
Let
and
. Then
and
. Thus we can express
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