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# Rearrange the differential equation into standard form.

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$$\frac{dP}{dt}=rP(1-\frac{P}{K})$$

Rearrange the differential equation into standard form.

I feel like I've attacked this every way possible but I can't seem to get into standard form.

Any help is greatly appreciated,

Thank you.

Mar 26, 2018

#1
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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...

Mar 26, 2018
edited by vest4R  Mar 26, 2018
#2
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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

Mar 26, 2018
#3
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thank you triggsy! just had a look at Partial Fraction Decomposition. Turns out they haven't taught us that yet.

thanks!

Mar 26, 2018
#4
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Thanks Tiggsy :)

Mar 26, 2018