- #1
Dustinsfl
- 2,281
- 5
[tex]\displaystyle\frac{dN}{dt} = rN\left(1-\frac{N}{K}\right)[/tex][tex]\displaystyle\int\frac{KdN}{N\left(K-N\right)} = \int rdt[/tex]
[tex]\displaystyle K\int\frac{dN}{N}-K\int\frac{dN}{K-N}=r\int dt[/tex]
Now, I obtain:
[tex]K\ln\left(\frac{N}{K-N}\right) = rt+c[/tex]
[tex]\left(\frac{N}{K-N}\right)^K=C_0r^{rt}[/tex]
The final solution is [tex]N(t) =\frac{C_0Ke^{rt}}{K+C_0(e^{rt}-1)}[/tex]
I don't see how I can manipulate my equation to that. Is there a mistake or am I not seeing something.
[tex]\displaystyle K\int\frac{dN}{N}-K\int\frac{dN}{K-N}=r\int dt[/tex]
Now, I obtain:
[tex]K\ln\left(\frac{N}{K-N}\right) = rt+c[/tex]
[tex]\left(\frac{N}{K-N}\right)^K=C_0r^{rt}[/tex]
The final solution is [tex]N(t) =\frac{C_0Ke^{rt}}{K+C_0(e^{rt}-1)}[/tex]
I don't see how I can manipulate my equation to that. Is there a mistake or am I not seeing something.
Last edited: