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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
. so . An integrating factor is
. 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
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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- Fall '08