# Understanding separable ODES

## Main Question or Discussion Point

I understand how to integrate this: ∫y2dy.

I dont understand how to integrate this:
di(t)/dt = i(t)p(t)
intergrate((di(t)/dt/i(t))*dt = p(t)dt) (see this image: http://i.imgur.com/OdKI309.png)

how do you perform the intergral on the left, seeing as as it not dt, but di(t)?

thanks

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Mark44
Mentor
I understand how to integrate this: ∫y2dy.

I dont understand how to integrate this:
di(t)/dt = i(t)p(t)
intergrate((di(t)/dt/i(t))*dt = p(t)dt) (see this image: http://i.imgur.com/OdKI309.png)

how do you perform the intergral on the left, seeing as as it not dt, but di(t)?

thanks
Can you do this integration? $\int \frac{du}{u}?$

BTW, there are no such words in English as "intergrate" and "intergral."

Can you do this integration? $\int \frac{du}{u}?$

BTW, there are no such words in English as "intergrate" and "intergral."
Yes I can do that.

But I do not understand how do integrate (what word do I use?)
∫di(t)/i(t)

Last edited:
Mark44
Mentor
Yes I can do that.

But I do not understand how do integrate (what word do I use?)
∫di(t)/i(t)
This is essentially the same as what I wrote.
$\int \frac{du}{u}$ is the same as $\int \frac{du(t)}{u(t)}$. The only difference is that in the second integral, it is made explicit that u is a function of t.

This is essentially the same as what I wrote.
$\int \frac{du}{u}$ is the same as $\int \frac{du(t)}{u(t)}$. The only difference is that in the second integral, it is made explicit that u is a function of t.
Thank you Mark!