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# integration watch

1. 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
3. (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
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.

Aah, it's been a long day of revision.
4. (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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