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anonymous
 5 years ago
Does does d(xy)/xy mean in regards to differential equations?
anonymous
 5 years ago
Does does d(xy)/xy mean in regards to differential equations?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0That just means the differential with respect to (xy), like du/u.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So how would I solve that on paper? Would I take the derivative of xy and then take the integral of the entire thing?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The whole problem is d(xy)/xy+dy=0

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hang on a sec  need to do something

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You can make it something more palatable for you by expanding the differential. That might be best. So, you'd write,

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\frac{d(xy)}{xy}=\frac{ydx+xdy}{xy}=\frac{dx}{x}+\frac{dy}{y}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The equation is \[\frac{dx}{x}+\frac{dy}{y}+dy=0 \rightarrow \frac{dx}{x}=(\frac{1}{y}+1)dy\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You can integrate this now.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\ln x = (\ln y +y)+c \rightarrow x=e^{\ln y  yc}=\frac{1}{y}e^{y}e^{c}=\frac{Ce^{y}}{y}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0+c in the exponentiation, but it doesn't matter since it just becomes the constant at the end.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You didn't do any integrating or differentation on that last part right? Just moved things around algebraically?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Note, this could have been obtained in a couple of steps from the first method I mentioned, namely,\[\frac{d(xy)}{xy}+dy=0 \rightarrow \ln xy +y = C \rightarrow xy.e^y=C \rightarrow x=\frac{C}{y}e^{y}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Which last part? Once the 'dx' and 'dy' differentials disappear, there's no more integration.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Nevermind. I think I see. I basically get the derivative of xy, which is 1. Then integrate 1/xy which is lnxy

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Why do you say the derivative of xy is 1?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Hmm .. doesn't one normally want the answer to a diff eq on the form y=... ? I see you wrote x=...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0If you saw \[\int\limits_{}{}\frac{du}{u}\]you'd know what to do. You'd recognize it as ln u.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Well, this would be transcendental in y, which is why it wasn't solved explicitly for y.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Re. the du/u integral, the d(xy)/(xy) thing is in the SAME FORM...so you do to it what you would do in the situation du/u.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I'm just having trouble figuring out with d(xy)/xy means. Is that just something I memorize du/u=ln u?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Okay, if I said, "The antiderivative of the differential of *something*, divided by that *something* is..?" what would you say to me?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the integral of f(x) / f(x) ?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0whatever we are integrating with repect to

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0lol, who's got a headache?

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0i just got here and i do

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Me. I've been struggling with this for over 10 hours now. I hate online school.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0In mathematics, it's all about *forms*.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0We always try to reduce more complicated problems into forms we already have solutions to.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0This is what we're doing here.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0We know that, whenever you have the form, \[\int\limits_{}{}\frac{d(something)}{(something)}\]the solution is \[\ln (something) + c\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Here the 'something' is (xy).

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0oh yes i get the something thing now

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok , so its just a form I need to memorize basically

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0But even better, understand how we get that form.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0But, look, if it's a pain for you and you stress in an exam, just expand the differential like I did above.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Unfortunetly thats just the tip of the iceberg in my lack of understanding. I'm in an 8 week online Calculus II class and struggling very badly.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0But thank you for the patience and the help. I think I understand a little bit better now.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0There's heaps of online resources. This site for one. Paul's Online Maths Notes are good, as well as www.khanacademy.org.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I've watched all those videos and looked. They help somewhat, but when I work specific problems I guess recognizing what method to use is where I struggle.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yes, that's called 'the problem of fluency' in mathematics. You need to do two things: 1) understand the mathematics and 2) recognize what you're being shown so you can access what you know. Sounds like number 2 is hassling you. That's good, though, because it can be fixed.

myininaya
 5 years ago
Best ResponseYou've already chosen the best response.0if I could become your fan again lokisan, i would

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Haha I think I'm also having difficulty in the understanding at some aspect as well. The bad part is I have little time to become fluent and understand before I move onto the next subject. I would also fan you 10 times.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hey, thanks myininaya ;)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Can I hire you over skype? lol

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0lol, just log on here. I lurk around.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The fluency part is 'easily' fixable because all it requires is doing problems.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0there are two types of problem: (1) closed and (2) open.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Well I'm doing them. For instance right now I'm trying to apply either seperation of variables or integrating combinations to this problem. I think I know what to do but I'm stuck

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0good stuff lokisan....... you couldn't have said it any better!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Closed problems are the ones you're probably used to, like, if the sides of a rectangle are 7 and 3 units, what's the perimeter? You can work that out easily since it's plug and play. But if someone says, "The perimeter of a rectangle is 20cm. What are it's dimensions?" people come unstuck.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Hmm ok well in that same topic then... what if you didn't have d(something/(something) and it was just d(something)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0For instance d(xy)=x/11 dx

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Well, Lokisan got one more fan for solving this differential eq :) I hadn't fanned him before (and is till now the only user here I am a fan of ;)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0re. your question scotty, what would you do if you saw,\[\int\limits_{}{}dx\]?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0My current problem is 11xdy+11ydx+xdx=0

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I know, I'm trying to make it easy on you.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I can move the xdx over, factor the 11 and then group xdy +ydx to be d(xy)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I would integrade which would be x

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Just give me a sec. to sort something nonmathematical out.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Okay, back. The reason I asked you about \[\int\limits_{}{} dx\]is because I wanted you to tie this idea of 'forms' from the last situation to this one. You've made life hard for yourself by going the route you did.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{}{}d(xy)=\int\limits_{}{}\frac{x}{11}dx \rightarrow xy=\frac{x^2}{22}+c \rightarrow y=\frac{x}{22}+\frac{c}{x}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0There's that 'form' thing going on again in d(xy).

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I think the route I went was the completely wrong way because that isn't the answer lol. According to my book its 22xy+x^2=C

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yeah, you can rearrange what I gave you.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.011xdy+11ydx+xdx=0 My first instinct is to want to move the xdx to the other side, but I already know this isn't seperable. So I need to use another method.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yes, you'll need a different method.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It's a lot messier than just recognizing the form of what you've been given and just exploiting it.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok so I think I can combine differentials to integrate them as a unit right? the 11xdy+11ydx can combine to form 11d(xy) right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok so from this point, can I just integrate each term?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Just like what I did above.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok so you're probably going to kill me, but d(xy) basically means the differential of our "function"?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0or do I just leave it alone? d(xy) just becomes xy..

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0lol, d(xy) means the differential of xy.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{}{}d(xy)=(xy)+c\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I think I'm getting hung up on the definition of a differential

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{}{}dw=w+c\]\[\int\limits_{}{}d(\cos \theta)=\cos \theta + c\]\[\int\limits_{}{}d(sty)=sty+c\]\[\int\limits_{}{}d(gp^4.78\frac{q}{a}+x^2e^{xy})=gp^4.78\frac{q}{a}+x^2e^{xy}+c\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I think that last thing you posted makes sense. I think I have it losesly in my mind what it means now

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0See what I keep doing, no matter how complicated it gets?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0If you sleep on it, it will sink in.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So it basically negates it. I got it. Thanks dude I'm going to try a few more examples
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