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    am really stuck with this function can you help me. i want the expression for
    N(t) and (t) from the the following

    ∫dN/dt= rN(1-N/k)-qN

    where r,k,q are constants
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    solution is badly neede
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    (Original post by mbukenya)
    am really stuck with this function can you help me. i want the expression for
    N(t) and (t) from the the following

    ∫dN/dt= rN(1-N/k)-qN

    where r,k,q are constants
    :dontknow: Better posting it in the Maths forum mate - lots of genius's there who will be able to help. I do double maths and I don't even understand the question lol. :rolleyes:

    Aah, it's been a long day of revision. :boring: :snoozing:
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    (Original post by mbukenya)
    am really stuck with this function can you help me. i want the expression for
    N(t) and (t) from the the following

    ∫dN/dt= rN(1-N/k)-qN

    where r,k,q are constants
    Assuming you mean,

    dN/dt= rN(1-N/k)-qN (with the ∫-sign at the beginning)

    dN/dt= rN -(r/k)N²-qN
    dN/dt= (r-q)N - (r/k)N²
    dN/dt = aN - bN²
    dN / (aN - bN²) = dt
    ∫ 1/(aN - bN²) dN = ∫ dt

    doing partial fractions work on 1/(aN - bN²) gives (1/a){1/N + b/(a - bN)}

    ∫ (1/a){1/N + b/(a - bN)} dN = ∫ dt
    (1/a){lnN - ln(a - bN)} = t - lnD :- lnD is const of integration
    ln{(DN)/(a - bN)} = at
    t = (1/a)ln{(DN)/(a - bN)}
    ====================

    a = (r - q)
    b = r/k
 
 
 
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