Rearrange the differential equation into standard form.

ultimately I have to solve it, but I should be right once it's in standard form.

I was thinking i'm being too picky and try to solve it with the separation methord. But I don't have an expression with t...

I don't know what you mean by 'standard form'.

Assuming that the p inside the bracket is the same as the P at the front,  the equation can be written as

\(\displaystyle \frac{dP}{dt}=\frac{rP}{K}(K-P),\)

from which we have, (assuming that the r and K are constants),

\(\displaystyle \int\frac{dP}{P(K-P)}=\frac{r}{K}\int dt.\)

Now it's a partial fractions job on the first integral.

Tiggsy

thank you triggsy! just had a look at Partial Fraction Decomposition. Turns out they haven't taught us that yet.

thanks!

Thanks Tiggsy :)