gah Quick math help

EDT 18:40 • CEST 00:40 • KST 07:40

Streams: 126 live
60870 total viewers

Active: 9668

General Discussion
TI3 East Qualifier Preview
The Defense Season 4 ann…
DotA 2 Team Recruitment …
TL's Item Trading Thread.
Dota 2 QQ thread

Dota 2 Tourneys

[TPL S5] Demon Edge Cup
[D2L] Na'Vi vs. Dignitas
Starladder Season 6
[The International] Easter…
Sticky Flames Weekly Dota …

Dota 2 Strategy

Simple Questions, Simple A…
Solo Mid - Who? What? How?
A guide to Krobelus, the D…
Newly ported Hero discussi…
[Guide] Storm Spirit by Bl…

BW General

Better Server Registry F…
[Update] itemBay SSL Gra…
snipealots 24/7 afreeca …
Making an Online Broodwa…
Pucca Comeback?
[TLS2] Qualifier #4 VODs

BW Tourneys

[GC S3] Gambit's Cup Semif…
Torenhire Starleague II
[TLS2] Qualifier #4
2x Speed Hack Perversion T…
Defiler Tour #57 [75$]

BW Strategy

Challenger map on Starcraf…
Simple Questions, Simple A…
Tips and tricks: Defilers …
Practice Partner Thread

Leta - Movie
Michael - skyline
Anytime - Beast
By.Hero - Shuttle
Anytime - Pusan

Customize Sidebar...

Website Feedback

Closed Threads

IRC Chat
irc.quakenet.org #teamliquid

IRC Web Client

TeamSpeak 3 (82 users)

Forum Index > Blogs

FragKrag United States. November 20 2009 14:00. Posts 11068

Profile Blog #

I have a math quiz tomorrow, and in the process of studying I found a problem that escapes me.

"Solve the differential equation by separation of variables."
essentially, integrate the function by separating y and x.

question:
dy/dx = cos(x) * e^(y + sin(x))

I get:
sin(x) = u, cos(x)dx = du

dy = du * e^(y + u)
dy = du * e^(y) * e^(u)
e^(-y)dy = e^(u)du

=>

-e^(-y) = e^(u) + C
ln(-e^(-y)) = ln (e^(u) + C)
y = ln(e^(u) + C)

answer is

y = - ln(C - e^(u))

Where the hell did I go wrong? :/

Last edit: 2009-11-20 14:02:10

*TL CJ Entusman #40* "like scissors does anything to paper except MAKE IT MORE NUMEROUS" -paper

mikeymoo Canada. November 20 2009 14:08. Posts 7064

Profile Blog #

-e^(-y) = e^u + C
e^(-y) = -e^u + C (C is an arbitrary constant anyway)
-y = ln(C-e^u)
y = -ln(C-e^u)

As for where your problem is, give me a second to figure that out.

I think it's your last line. ln(-e&(-y)) != y
ln(-e^(-y)) = (ln(e^(-y))^(-1) = -y^(-1) ?

o_x | Ow. | 1003 ESPORTS dollars | If you have any questions about bans please PM Kennigit

igotmyown United States. November 20 2009 14:11. Posts 2883

Profile Blog #

ln(-e^(-y)) = ln (e^(u) + C) is illegal

FragKrag United States. November 20 2009 14:11. Posts 11068

Profile Blog #

oh I didn't realize I took the ln of a negative

thanks!_!

So the negative doesn't affect the constant? fuuuuu

tytyty

Last edit: 2009-11-20 14:12:01

*TL CJ Entusman #40* "like scissors does anything to paper except MAKE IT MORE NUMEROUS" -paper

Turbovolver Australia. November 20 2009 14:16. Posts 1637

Profile Blog #

I get the feeling you should definitely move the negative over before taking the ln of both sides. You don't want to take ln of negative numbers, and the left hand side is definitely negative.

If you do move the negative over, you will get

ln(e^(-y)) = ln (-e^(u) + D) (new constant which would be the negative of your old one)

And now, you will get their answer.

It's really weird though, it feels like it should still technically be "legal" to do it your way.

edit: I'm too slow.

The negative affects the constant but you just relabel it as a new constant. For all you knew C was negative anyway, so your new one is a positive constant.

Last edit: 2009-11-20 14:18:36

The original Bogus fan.

FragKrag United States. November 20 2009 14:18. Posts 11068

Profile Blog #

I completely just breezed over it somehow, and I never realized that a negative doesn't "affect" the constant, though it does make sense now that I've seen it.

i <3 tl

Last edit: 2009-11-20 14:18:49

*TL CJ Entusman #40* "like scissors does anything to paper except MAKE IT MORE NUMEROUS" -paper

coltrane Chile. November 20 2009 16:57. Posts 986

Profile Blog #

lol you always add the constant because you dont even know if is positive in the first place. Actually, it doesnt matters, the algebra>>>>the signus.

Jävla skit

evanthebouncy! United States. November 20 2009 18:49. Posts 10736

Profile Blog #

here, cheer you up

Life is run, it is dance, it is fast, passionate and BAM!, you dance and sing and booze while you can for now is the time and time is mine. Smile and laugh when still can for now is the time and soon you die!

Please log in or register to reply.