Ordinary Diff Eq Exam Review Solutions 31

Ordinary Diff Eq Exam Review Solutions 31 - 1 Solutions...

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Unformatted text preview: 1 Solutions gives . Integrating gives . Since and hence 33 we have . 14. Note that is a solution. Divide both sides by . Let . Then and hence standard form we get gives . Solving for we can solve for we get which is a Bernoulli equation with is not a solution. Dividing by , . Let . Then and in standard form we get . Integration gives we get . so . An integrating factor is so so . Since to get . Since get . Since . gets us back to with and integrating to get 15. If we divide by we get . Note that since 16. First divide by , which is a Bernoulli equation , . Let is not a solution. Now divide by . Then factor is . Multiplying by Integration by parts gives , . we have . Let we get . An integrating gives and thus . . Since is a solution. First divide both sides by . Then to and substituting gives . In standard form we get 17. Note that . In . The integrating factor is . Multiplying by gives to get . So to get . In standard form . An integrating factor is and hence . Integration by parts gives hence . Since 18. The logistic differential equation is . Note that and we get . which can be written is a solution. Divide by to get ...
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