Ordinary Diff Eq Exam Review Solutions 6

# Ordinary Diff Eq Exam Review Solutions 6 - 8 1 Solutions 33...

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Unformatted text preview: 8 1 Solutions 33. From Problem 20 the general solution is we get . 34. From Problem 21 the general solution is . It follows that get . At . It follows that and . At we and . 35. From Problem 24 the general solution is we get . It follows that . 36. From Problem 27 the general solution is at gives . Hence 37. From Problem 28 the general solution is at gives so . At and . Evaluation and . Evaluation . . Hence 38. From Problem 31 the general solution is a . Evaluation at . If follows that . 39. Implicit diﬀerentiation with respect to gives 40. Implicit diﬀerentiation with respect to gives gives and and and . Thus . . 41. Diﬀerentiation gives . However, from the given function we have . Substitution gives . 42. Diﬀerentiation gives we have . and hence . However, from the given function . Substitution gives ...
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