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Understanding separable ODES

  1. Jan 25, 2015 #1
    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
     
  2. jcsd
  3. Jan 25, 2015 #2

    Mark44

    Staff: Mentor

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

    BTW, there are no such words in English as "intergrate" and "intergral."
     
  4. Jan 25, 2015 #3
    Yes I can do that.

    But I do not understand how do integrate (what word do I use?)
    ∫di(t)/i(t)
     
    Last edited: Jan 25, 2015
  5. Jan 26, 2015 #4

    Mark44

    Staff: Mentor

    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.
     
  6. Jan 26, 2015 #5
    Thank you Mark!
     
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