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**Chapter 4 / 4.2 question 28**

« **on:**October 24, 2020, 05:37:35 PM »

Hi, I was wondering if anyone had figured out how to factor the characteristic polynomial for this ODE. Thanks!

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Hi, I was wondering if anyone had figured out how to factor the characteristic polynomial for this ODE. Thanks!

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I could be wrong, but I think we just try each one until we get one that works

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Sorry, I think I asked my question in the wrong folder!!! Here is my question:

Hi, I'm having a lot of trouble with questions 14 and 15. I know how to find the solution, but I don't know how to do the rest, can someone please help??

Hi, I'm having a lot of trouble with questions 14 and 15. I know how to find the solution, but I don't know how to do the rest, can someone please help??

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I asked Victor and he said either is fine, depending on which is more convenient.

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Add all those terms on both sides so they're all positive instead (just make to make it easier), and then combine the ln|x| and ln|y/x+1| using product rule for logarithms (i.e., log(a)+log(b)=log(ab)).

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Ah, I just read 2.4 in the textbook and the Existence and Uniqueness Theorem. I get it now, thank you for trying to make me understand it

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Still don't get it . If we let this range be all real numbers t excluding t=-ln2, the initial condition would still be included in that. Is just the fact that there's an asymptote at -ln2 and therefore everything left of t=-ln2 isn't "connected" to the part of the solution that has the point (0,-1)? In other words, we're including the only continuous portion?

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I'm sorry, I still don't understand why we can ignore t<-ln2 just because the initial condition is y(0)=1

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I think you didn't do the partial fraction decomposition correctly, 1/y(y-1) = -1/y + 1/(y-1). I got 1/(1-ce^x) as my general solution

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Thank you so much!

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Hi, the solution to this differential equation is c=|y+x||y+4x|^2 (according to the textbook solutions), but I have a slightly different answer (essentially, I got cx^2=|y+x||y+4x|^2 instead of just c) and I'm not sure where I'm going wrong. Can someone please help me? Thanks!

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