anonymous
  • anonymous
Need help with differential equations :/. Find a second solution for xy''+(x-1)y'-y=0, given that y1=e^-x.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
Do you know how to use integrating factor?
anonymous
  • anonymous
Oh... yes I do but I thought that only worked if the equation was in standard form and a first order equation. y'+P(x)y=q(x)
anonymous
  • anonymous
In that case I would just multiply everything by e^(integral (p) dx). Does that work on this too?

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anonymous
  • anonymous
Ah wait do I need to do reduction of order to get it in the right form?
anonymous
  • anonymous
Oh wait, give me a few minutes. I'm not sure if it applies here.
anonymous
  • anonymous
okay thank you. I appreciate it because I am definitely lost :/.
anonymous
  • anonymous
I actually am taking Differential Equations right now for my engineering major, but we haven't covered second order differential equations with nonconstant coefficients. I would recommend however visiting this page http://tutorial.math.lamar.edu/Classes/DE/ReductionofOrder.aspx It seems to be close to what you are looking for. :)
anonymous
  • anonymous
Okay I will read over it right now. Thank you for the link :). and that is interesting. I studied molecular biology but I am switching to biosystems engineering.
anonymous
  • anonymous
If they were constants, I'd totally be able to help you using the different cases :) I can't do anything biology for the life of me, haha. I admit I find it extremely fascinating but I can never memorize all the terms and functions XD
anonymous
  • anonymous
hmm... okay so I did find an answer key to the question but I am still not sure how the professor solved this. Apparently the answer is y2=x-1 but I am still trying to figure out what she did.
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anonymous
  • anonymous
I think I understand the basic idea a solution to the differential equation can be a scalar multiple of the given y1. but I don't understand where the integrating factor comes in... this is so frustrating :/.
anonymous
  • anonymous
I don't understand why he used integrating factor at first. It seems like a different method than reduction of order, but I actually understand what he's doing. It seems like after finding e^-u, he integrating in the following form \[y_2=y_1* \int\limits \frac{ e^{-\mu} }{ y_1{^2} }dx\] Then once he simplified that, he just plugged in y1 that was given from the beginning. Also note that at the end, he put an e^-x instead of e^x for the last term in the parentheses. Or vice versa. Not sure which one it's suppose to be but there's an error there.
anonymous
  • anonymous
Does this make sense now?
anonymous
  • anonymous
I sort of understand but I don't really get why the professor is multiplying by ∫e^(−μ)/y^2)dx. Where does that come from?
anonymous
  • anonymous
I'm assuming it's some sort of formula to follow. I wouldn't really know because I haven't learned this yet (until now though, so thank you :P). But I don't understand the logic behind it and where it was derived from. For now I would just go with it and ask your professor later for clarification.
anonymous
  • anonymous
haha... okay... well, if it works on the exam, I won't question it lol.
anonymous
  • anonymous
:)
anonymous
  • anonymous
Thanks for the help :). Good luck with your studies as well. Hopefully we can help eachother out :p
anonymous
  • anonymous
You are very welcome! And hopefully :P

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