if a differential equations solution divides by x^2 and the initial condition is a point where x=0, what do you do? (problem: dy/dx=xyy or dy/dx=xy^2)

- anonymous

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- anonymous

initial condition is (0,-2)

- anonymous

You can use separation by variables here and then integrate. Once you have y after integration, you can use the initial condition.

- anonymous

i did that, but my solution is y=(-2/x^2)+2
which doesnt technically do through the initial condition

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## More answers

- anonymous

i think its a vertical asymptote which... definitely isint the point XD

- anonymous

There's nothing wrong with that equation. After you put it into separable form and solve, you should get,\[\frac{x^2y}{2}+cy+1=0\]Initial condition,\[0-2c+1=0 \rightarrow c=\frac{1}{2}\]

- anonymous

You can then factor out y and rearrange into the form y=y(x).

- anonymous

brb

- anonymous

i got c=2?

- anonymous

When you separated the variable and tried to get y by itself did you include c and also multiply the y by it?

- anonymous

.... -.-

- anonymous

ima try that, how about: y'=1+yy

- anonymous

You can do that problem the same way. I look at it as y' is dy/dx and then separate variables. Make sure when you do though, that the 1 goes with the y^2. So move the entire quantity.

- anonymous

dang, the small things get by me... that should be something like arctany=x+c? so tan(x+c)=y?

- anonymous

that explains why my condition is in radians

- anonymous

Yes.

- anonymous

alright... major confusion...
\[y'=(e ^{x-y})\div(1+e ^{x})\]

- anonymous

You want to solve that?

- anonymous

sadly ><

- anonymous

Just pull out the e^(-y) and it becomes separable ;)

- anonymous

asoghaqoeraifoiafauirfhlanihusdfvnnfldanufd

- anonymous

\[e^ydy=\frac{e^x}{1+e^x}dx\]

- anonymous

differential equations are gay -.-

- anonymous

lol

- anonymous

dont tell me any more!!!

- anonymous

tell you what? answers?

- anonymous

yeah.. dont tell me any more lol

- anonymous

no worries :D

- anonymous

I think you have the best icon...if that helps...

- anonymous

hahahaha it was annoyingly hard to make XD

- anonymous

i have a pretty good feeling that your icon is not you... though there is a significant chance that i am wrong given by the circumstances

- anonymous

it could be me, since i look like that

- anonymous

lol, how did your frigging doughnut go?

- anonymous

pretty good, i have a way of doing things when i need help: use the first sentence or line of the help, fail a thousand times before i use the second, so on and so forth. so i used quite a bit, but not all of your help in the process of doing the assignment, and in the end i was flowing through it quite nicely, i compared my results to yours and they were identical, i then compared my results to the assignment and apparently the last couple steps, which i had done by hand, i could take the integral with a calculator... and then later he gave us the hand written answer, so i felt proud that i did it without a calculator... but yeah your help is insanely apreciated

- anonymous

alright im stuck at e^y=ln(1+e^x)+c
initial condition is (0,1)

- anonymous

Is that y supposed to be y' (y-prime)?

- anonymous

nope, thats my solution

- anonymous

to the above equation

- anonymous

oh..

- anonymous

Yeah. You're right. Leave it like that too.

- anonymous

but i need to find c

- anonymous

Oh, just plug your numbers in.

- anonymous

\[e=\ln 2 +c \rightarrow c = e- \ln 2\]

- anonymous

any way to do that without a calc?

- anonymous

You mean simplify?

- anonymous

No.

- anonymous

What's wrong with Euler's number? :p

- anonymous

ah god its 1... can you check these real quick?

- anonymous

Check what?

- anonymous

Do you ever sleep?

- anonymous

##### 1 Attachment

- anonymous

not too much anymore lol

- anonymous

I need paper...I've run out...hang on...

- anonymous

but all my work is shown?

- anonymous

I get something different for the first one. Just go to bed and I'll look at it and scan and you can look at it when you get up.

- anonymous

do i have to multiply the c by 2 aswell?

- anonymous

I'll do it here:

- anonymous

my answer doesnt make sense anyways... when i find y' its all weird and quotienty

- anonymous

\[\frac{dy}{dx}=xy^2 \rightarrow y^{-2}dy = x dx \rightarrow -y^{-1}=x+c\]

- anonymous

Your boundary condition is (0,-2), so

- anonymous

x+c or (1/2)xx+c?

- anonymous

\[-2^{-1}=0+c \rightarrow c=-\frac{1}{2}\]

- anonymous

So\[y^{-1}+x=\frac{1}{2} \rightarrow 2+2xy=y \rightarrow y(1-2x)=2 \rightarrow y=\frac{2}{1-2x}\]

- anonymous

waitttt the integral of xdx is (1/2)xx+c though!

- anonymous

Oh crap, I forgot the frigging x. Sorry Arman.

- anonymous

nah dont be sorry, i should hit the sheets tho, i'll probably have more questions tomorrow lol

- anonymous

I still get a different answer to you.

- anonymous

basic differential equations (like these) arent usually part of calc II are they?

- anonymous

Yours is close. I'll work through them - they won't take long - and scan and you can read it in the morning.

- anonymous

different answer?

- anonymous

I'm not sure about the American system.

- anonymous

y=2/(1-x^2)

- anonymous

did you use (0,-2) for the initial whatever?

- anonymous

pellet, I wrote it wrong on my paper. I wrote (0,2). SORRY AGAIN :'(

- anonymous

NOW I get what you got.

- anonymous

>< nah man i hate when ppl tell me sorry

- anonymous

lol XD

- anonymous

my calc teacher, this morning, was like "oh flutter..." *covers mouth*... *whole class starts laughing
caus we hear him say pellet sometimes but never the f word so it meant he was really screwed over XD

- anonymous

lol, it's great when that happens.
I got the same results as you for the other two. The *only* thing I would do differently is leave \[e-\log 2\]as is, and not use a numerical approximation (in the last one).

- anonymous

thats probably better in the math world, where you need to be precise

- anonymous

Yeah, exactly.

- anonymous

is that prefered in college?

- anonymous

preferred*

- anonymous

Absolutely. You'd only use a numerical approximation for the time you actually need to extract a number. Other than that, we leave it because we may want to do further mathematics on it and we lose information/exactness if we start approximating beforehand.

- anonymous

just like the AP exams lol. i think i asked you before but what are the remaining major math courses after differential eqas and linear algebra (when i say top i mean like... there should be less than 3 "top" ones)

- anonymous

?

- anonymous

Yeah, I really don't know. Your system is different to the system in UK, Australia and Canada. We don't break mathematics up into sections like calculus and then apply a skill level to it. We apply a skill level to ALL of mathematics at particular points and you learn EVERYTHING at a particular level.

- anonymous

oh... well what are the chances that i can attain a college grad level (in math) of mathematical understanding in the next year?

- anonymous

given the rate that i covered calc 1 and 2 within 1.5 months

- anonymous

I'd say you're pretty good.

- anonymous

College grad level in calculus...is that what you're asking?

- anonymous

You have to cover calculus of a complex variable as well. There's also tensor calculus.

- anonymous

not just calculus, but all mathematics, can i attain that sort of knowledge, about 4 or more years of college math in the next 9 months?

- anonymous

complex variable wont be too hard, what is tensor calc??

- anonymous

It *might* take a little longer ;p

- anonymous

They're devices we use to extend scalars, vectors and matrices to higher dimensions.

- anonymous

They're very useful.

- anonymous

http://www.dailymail.co.uk/news/article-1369595/Jacob-Barnett-12-higher-IQ-Einstein-develops-theory-relativity.html

- anonymous

my goal, i am currently 11 years behind

- anonymous

It also depends on what areas you want to focus on in maths. There's discrete mathematics/number theory, mathematical logic, topology, algebra, mathematical statistics,...

- anonymous

Yeah, I'be heard of him. I hope you get there (minus the autism).

- anonymous

*I've*

- anonymous

We 'know' general relativity is wrong - feel like fixing it, Arman?

- anonymous

sounds like a plan

- anonymous

What about bed?

- anonymous

Might be the first step.

- anonymous

oiudhvcapoufimnac

- anonymous

Is that code?

- anonymous

fine -.-

- anonymous

lol

- anonymous

nah, gibberish.... alright my chances of catching up to an ausbergers kid is highly unlikely, but i can at least try to match his pace...

- anonymous

i think... idk. i will win -.-

- anonymous

yeah, that's the right attitude

- anonymous

Just ace your doughnuts.

- anonymous

lol iight gnight yo

- anonymous

nite

- anonymous

hey arman

- anonymous

I am becomeMyFan lol, got a new account because I got tired of my old name

- anonymous

hey loki=D

- anonymous

hello

- anonymous

how are you doin?

- anonymous

do you like my new name LOL

- anonymous

ok. bit tired. should be doing my work but wasting time

- anonymous

Yeah, it's cool...did BMF die?

- anonymous

yeah

- anonymous

sad

- anonymous

RIP, BMF

- anonymous

LOL =D, or as sstarica says it, ^_^

- anonymous

Is oktalBlizzard meant to mean something?

- anonymous

i just fanned you

- anonymous

All that work you did collecting fans, gone!

- anonymous

well, it is just my internet user name/ nick name.Oktal means base 8, and blizzard is a natural disaster LOL, thanx I fanned you too, the 132nd fan

- anonymous

=D yeah

- anonymous

As in base 8 for numbers?

- anonymous

but now I am planning to help people more once I learn some more stuff and write my exams

- anonymous

yes, for numbering system, like binary, octal, hexadecimal...

- anonymous

Cool.../random

- anonymous

well, I wanted it to be a bit diferent then my usual nicks

- anonymous

Arman's gone to bed

- anonymous

:)

- anonymous

How's the studying?

- anonymous

great

- anonymous

wow, you're probably the first person i've even asked that question who's said that

- anonymous

:) but really it is great, because I made up my mind to enjoy maths and physics and stuff like this

- anonymous

it is all about the attitude, I think

- anonymous

lol

- anonymous

it is

- anonymous

research backs it

- anonymous

If you assume, when you get to something in maths that you don't understand, that you can understand it eventually, well, the research says those people are more successful.

- anonymous

Took longer to say that than I had anticipated.

- anonymous

Remains of the day.

- anonymous

I just looked at my About me, and noticed something LOL, "...I have infinite interesting ideas but my limit is time..." coincidense but that actually reminds me of something I have learned in maths

- anonymous

lol

- anonymous

Should you be studying versus helping others?

- anonymous

well, I am actually solving questions my self, but once every hour or something I come here to solve a problem or two, to change the mental environment.

- anonymous

lol, okay. you seem sorted.

- anonymous

\[\sum_{\lim_{n \rightarrow \infty}}^{n} n\]
where n is ideas
something like this?
can you improve it?

- anonymous

You could just say\[\left| \left\{ I_{oB} \right\} \right|=\infty\]

- anonymous

The cardinality (size) of the set of oktalBlizzard's ideas is infinite.

- anonymous

:) nice

- anonymous

too bad we can include maths symbols in about me text

- anonymous

You can refer people here to get a better idea.

- anonymous

=D

- anonymous

so, have you checked out the new study groups? Physics, Chemistry and Computer Science?

- anonymous

I had a look at physics yesterday and I was the only one online

- anonymous

me too

- anonymous

I haven't looked at the others.

- anonymous

I don't know anything else about the other subjects. Well, enough to offer any advice.

- anonymous

Q: How does one insult a mathematician?
A: You say: "Your brain is smaller than any ε > 0"

- anonymous

lol, that's pretty good.

- anonymous

Theorem: Every positive integer is interesting.
Proof: By contradiction, assume that there exists an uninteresting positive integer. Then there must be a smallest uninteresting positive integer. But that's pretty interesting! Therefore a contradiction!

- anonymous

Let epsilon be less than zero...

- anonymous

Are you coming up with this random stuff?

- anonymous

In some alley, a function meets up with a differential operator:
"Get out of my way - or I'll differentiate you till you're zero!"
"Try it - I'm \[e ^{x} \]..."
"Too bad... I'm d/dy."
no, I got this from a friend

- anonymous

I have one.

- anonymous

Pi had an argument with i.
i told pi to be rational and
pi told i to get real

- anonymous

Nice! LOL, I think I heared something like that,
Check this:
Salary Theorem: The less you know, the more you make.
Proof:
Fact #1: Knowledge is Power
Fact #2: Time is Money
We know that: Power = Work / Time
And since Knowledge = Power and Time = Money
It is therefore true that Knowledge = Work / Money
Solving for Money, we get:
Money = Work / Knowledge
Thus, as Knowledge approaches zero, Money approaches infinity, regardless of the amount of Work done

- anonymous

Yeah, I think that's more sadly true than funny ;p

- anonymous

aiight OB, I have to go. Have to do some work before the days runs out and I feel guilty ;)

- anonymous

he also gave me this, but I dont get it at all, maybe you do:
A SLICE OF PI
******************
3.14159265358979
1640628620899
23172535940
881097566
5432664
09171
036
5
ok, bye, see you next time

- anonymous

hehe..see you :)

- anonymous

lolol

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