## anonymous 5 years ago 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)

1. anonymous

initial condition is (0,-2)

2. anonymous

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

3. anonymous

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

4. anonymous

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

5. 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,$0-2c+1=0 \rightarrow c=\frac{1}{2}$

6. anonymous

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

7. anonymous

brb

8. anonymous

i got c=2?

9. anonymous

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

10. anonymous

.... -.-

11. anonymous

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

12. 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.

13. anonymous

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

14. anonymous

that explains why my condition is in radians

15. anonymous

Yes.

16. anonymous

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

17. anonymous

You want to solve that?

18. anonymous

19. anonymous

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

20. anonymous

asoghaqoeraifoiafauirfhlanihusdfvnnfldanufd

21. anonymous

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

22. anonymous

differential equations are gay -.-

23. anonymous

lol

24. anonymous

dont tell me any more!!!

25. anonymous

26. anonymous

yeah.. dont tell me any more lol

27. anonymous

no worries :D

28. anonymous

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

29. anonymous

hahahaha it was annoyingly hard to make XD

30. 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

31. anonymous

it could be me, since i look like that

32. anonymous

lol, how did your frigging doughnut go?

33. 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

34. anonymous

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

35. anonymous

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

36. anonymous

nope, thats my solution

37. anonymous

to the above equation

38. anonymous

oh..

39. anonymous

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

40. anonymous

but i need to find c

41. anonymous

Oh, just plug your numbers in.

42. anonymous

$e=\ln 2 +c \rightarrow c = e- \ln 2$

43. anonymous

any way to do that without a calc?

44. anonymous

You mean simplify?

45. anonymous

No.

46. anonymous

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

47. anonymous

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

48. anonymous

Check what?

49. anonymous

Do you ever sleep?

50. anonymous

51. anonymous

not too much anymore lol

52. anonymous

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

53. anonymous

but all my work is shown?

54. 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.

55. anonymous

do i have to multiply the c by 2 aswell?

56. anonymous

I'll do it here:

57. anonymous

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

58. anonymous

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

59. anonymous

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

60. anonymous

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

61. anonymous

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

62. anonymous

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

63. anonymous

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

64. anonymous

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

65. anonymous

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

66. anonymous

I still get a different answer to you.

67. anonymous

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

68. anonymous

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

69. anonymous

70. anonymous

I'm not sure about the American system.

71. anonymous

y=2/(1-x^2)

72. anonymous

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

73. anonymous

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

74. anonymous

NOW I get what you got.

75. anonymous

>< nah man i hate when ppl tell me sorry

76. anonymous

lol XD

77. 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

78. 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).

79. anonymous

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

80. anonymous

Yeah, exactly.

81. anonymous

is that prefered in college?

82. anonymous

preferred*

83. 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.

84. 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)

85. anonymous

?

86. 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.

87. anonymous

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

88. anonymous

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

89. anonymous

I'd say you're pretty good.

90. anonymous

91. anonymous

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

92. 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?

93. anonymous

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

94. anonymous

It *might* take a little longer ;p

95. anonymous

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

96. anonymous

They're very useful.

97. anonymous
98. anonymous

my goal, i am currently 11 years behind

99. 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,...

100. anonymous

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

101. anonymous

*I've*

102. anonymous

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

103. anonymous

sounds like a plan

104. anonymous

105. anonymous

Might be the first step.

106. anonymous

oiudhvcapoufimnac

107. anonymous

Is that code?

108. anonymous

fine -.-

109. anonymous

lol

110. 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...

111. anonymous

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

112. anonymous

yeah, that's the right attitude

113. anonymous

114. anonymous

lol iight gnight yo

115. anonymous

nite

116. anonymous

hey arman

117. anonymous

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

118. anonymous

hey loki=D

119. anonymous

hello

120. anonymous

how are you doin?

121. anonymous

do you like my new name LOL

122. anonymous

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

123. anonymous

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

124. anonymous

yeah

125. anonymous

126. anonymous

RIP, BMF

127. anonymous

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

128. anonymous

Is oktalBlizzard meant to mean something?

129. anonymous

i just fanned you

130. anonymous

All that work you did collecting fans, gone!

131. 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

132. anonymous

=D yeah

133. anonymous

As in base 8 for numbers?

134. anonymous

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

135. anonymous

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

136. anonymous

Cool.../random

137. anonymous

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

138. anonymous

Arman's gone to bed

139. anonymous

:)

140. anonymous

How's the studying?

141. anonymous

great

142. anonymous

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

143. anonymous

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

144. anonymous

it is all about the attitude, I think

145. anonymous

lol

146. anonymous

it is

147. anonymous

research backs it

148. 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.

149. anonymous

Took longer to say that than I had anticipated.

150. anonymous

Remains of the day.

151. 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

152. anonymous

lol

153. anonymous

Should you be studying versus helping others?

154. 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.

155. anonymous

lol, okay. you seem sorted.

156. anonymous

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

157. anonymous

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

158. anonymous

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

159. anonymous

:) nice

160. anonymous

161. anonymous

You can refer people here to get a better idea.

162. anonymous

=D

163. anonymous

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

164. anonymous

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

165. anonymous

me too

166. anonymous

I haven't looked at the others.

167. anonymous

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

168. anonymous

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

169. anonymous

lol, that's pretty good.

170. 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!

171. anonymous

Let epsilon be less than zero...

172. anonymous

Are you coming up with this random stuff?

173. 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

174. anonymous

I have one.

175. anonymous

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

176. 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

177. anonymous

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

178. anonymous

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

179. 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

180. anonymous

hehe..see you :)

181. anonymous

lolol