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Ordinary Diff Eq Exam Review Solutions 104

# The general solution is 2 a fundamental set for is

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Unformatted text preview: ral solution is 2. A fundamental set for is . Then the matrix equation . Let and implies and hence and . Now . Since is a homogeneous solution we can write the general solution as . On the other hand, the incomplete partial fraction method gives that a particular solution is . 3. The functions . From this we see . The general solution is and form a fundamental set. Let . Then the matrix equation implies that and . Hence, and . From this we get . On the other hand, the method of undetermined coeﬃcients implies that a particular solution is of the form . Substitution gives and hence . It follows that . Furthermore, the general solution is...
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