Ordinary Diff Eq Exam Review Solutions 97

# Ordinary Diff Eq Exam Review Solutions 97 - 1 Solutions 99...

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Unformatted text preview: 1 Solutions 99 . It follows that the Wronskian is zero for all . 3. The condition that the coeﬃcient function be nonzero in Theorem 4 and Proposition 6 is essential. Here the coeﬃcient function, , of is zero at , so Proposition 6 does not apply on . The largest open intervals on which is nonzero are and . On each of these intervals and are linearly dependent. 4. Consider the cases and . The veriﬁcation is then straightforward. 5. Again the condition that the coeﬃcient function be nonzero is essential. The Uniqueness and Existence theorem does not apply. Section 4.3 1. The indicial polynomial is two distinct roots and . The fundamental set is solution is 2. The indicial polynomial is two distinct roots . There are . The general . There are and . The fundamental set is . The general solution is 3. The indicial polynomial is root, . There is one , with multiplicity . The fundamental set is . The general solution is . There are 4. The indicial polynomial is two distinct roots and . The fundamental set is . The general solution is 5. The indicial polynomial is . The root is with multiplicity . The fundamental set is . The general solution is 6. The indicial polynomial is are and . The fundamental set is . The roots . The general solution is 8. The indicial polynomial is . There are two complex roots, The fundamental set is and . . The general solution is ...
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