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Messages - Xinyi Li

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MAT244 Math--Lectures / Integrating Factor of Exact Equations
« on: October 06, 2014, 05:53:39 PM »
Hi all,

Is the integrating factor for exact equations covered so far?
I did not find those in my lecture notes, but found it in the text book and some past exams.

Thanks in advance.

MAT244 Misc / Problem With inserting Pictures when reply
« on: September 27, 2014, 08:05:46 PM »

Could anyone give me some instructions on inserting image in the reply.
It's like the html format, but when I type in the image location, it just won't read it.
It the only way to insert a picture is by attachment?

Thanks for your helps in advance.

MAT244 Math--Lectures / Re: 1.1 28
« on: September 27, 2014, 08:03:08 PM »
Based on my understanding, the directional field is purely described by this equation only: y^'=e^(-t)+y
From the equation we can see that, when y=0 and t→+infinity y’ will goes to 0. That is the only place that the directional field will have horizontal lines meaning zero slope. The answer should be something like the attachment.

For the general solution, clearly the prof has helped us confirmed is:
So if we set c = 0, then we will easily find an equilibrium solution for the ODE. I think you have a little misunderstanding with the directional field. You can look at the original post, professor Victor has given a pretty clear answers. Hope this can help.

MAT244 Math--Lectures / Re: Problem 1.1.28
« on: September 17, 2014, 11:26:02 AM »
Thanks for explaining.
Yeah, i think i am using too easy theories to look at the questions.
Thanks for pointing out, now I can see the whole picture.
Big helps~

MAT244 Math--Lectures / Re: Problem 1.1.28
« on: September 16, 2014, 01:44:47 PM »
Hi, I think you have mixed up something here.
For the directional field, when y = 0, if you let t goes from -infinity to +infinity,
the slope y' basically follow the function e^(-t) which finally approach 0 at some point.

That means for function y, although it keep increasing but the rate of increasing is keep getting smaller. Just like the -e^(-t) function, it keep increasing for t increases, but finally it approaches 0.You can definitely see it approaches 0 though the directional filed graph without any calculation of the solution. I don't see any confusion here.


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