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Math Help - solving the differential equation...

  1. #1
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    solving the differential equation...

    ok here we go...

    the rate of change of N with respect to S is proportional to 500 - S

    so the set up is pretty straight forward...

    I got dN/dS = k(500 - S)

    when i integrated it i got N = 500S - (S)^2/2 + C, the book said something different..which is where im confused..

    books answer: N = -k/2(500 - S)^2

    please explain, thanks in advance....
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  2. #2
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    Quote Originally Posted by slapmaxwell1 View Post
    ok here we go...

    the rate of change of N with respect to S is proportional to 500 - S

    so the set up is pretty straight forward...

    I got dN/dS = k(500 - S)

    when i integrated it i got N = 500S - (S)^2/2 + C, the book said something different..which is where im confused..

    books answer: N = -k/2(500 - S)^2

    please explain, thanks in advance....
    Check to see if the problem didn't say
    "the rate of change of N with respect to S is inversely proportional to 500 - S".
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  3. #3
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    ok it said proportional....
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  4. #4
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    the book says,

    dN/ds = k(500 - s)

    dN/ds = k(500- s)

    ∫▒dN/ds ds= ∫▒〖k(500-s)ds〗

    ∫▒dN= - k/2 (500 - s)^2 + C
    N= -k/2 (500-s)^2+C
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