• Today, 15:31
Yes, but you used it on the original ODE, not the one in standard linear form. :)
4 replies | 58 view(s)
• Yesterday, 07:29
Wilmer replied to a thread Present Value Maths in Other Topics
Book is correct. Are you using a calculator? You're probably entering the data wrongly...we can't tell... Try it this way: u = (1.02/1.10)^10 v =...
2 replies | 56 view(s)
• Yesterday, 06:19
Thanks steenis ... No worries at all ... Thanks for all your help ... Peter
10 replies | 172 view(s)
• Yesterday, 06:04
Thanks Steenis ... That proof seems really clear ... Will work through it again shortly... Peter
4 replies | 75 view(s)
• Yesterday, 05:18
Sorry Steenis ... I don't understand you ... Can you give me a hint as to what is wrong ...? Peter
10 replies | 172 view(s)
• Yesterday, 04:51
Thanks steenis ... most helpful ... Can see that the short exact sequence $0\rightarrow \text{ker } f \overset{i}{ \rightarrow}R^{(n)}... 10 replies | 172 view(s) • Yesterday, 01:22 ======================================================================== Since I could not see any specific errors, I have completed the proof... 4 replies | 75 view(s) • June 17th, 2018, 14:46 I have thought of the following algorithm: We put an antenna$k$meters east of the westernmost house. We continue to the east, by placing an... 1 replies | 38 view(s) • June 17th, 2018, 12:39 MarkFL replied to a thread [SOLVED] 2.2.3 de with tan x in Differential Equations I can't imagine trying to use the internet on a telephone. I'm sorry scrolling on a telephone is such a chore...they should fix that. 8 replies | 107 view(s) • June 17th, 2018, 11:00 Hello!!! (Wave) We consider a long country road with$n$houses placed along of it (we think of the road as a big line segment). We want to put... 1 replies | 38 view(s) • June 17th, 2018, 05:04 Peter started a thread Deveno ... in Chat Room Deveno is much missed ... especially by those who frequent the Linear and Abstract Algebra Forum ... Deveno's pedagogical abilities were as... 0 replies | 44 view(s) • June 17th, 2018, 04:40 I am reading Dummit and Foote's book: "Abstract Algebra" (Third Edition) ... I am currently studying Chapter 10: Introduction to Module Theory ...... 4 replies | 75 view(s) • June 17th, 2018, 00:59 MarkFL replied to a thread [SOLVED] 2.2.3 de with tan x in Differential Equations Are you using Tapatalk by any chance? I have code in place to let me know when posts have been edited, so I don't miss added content (it's better to... 8 replies | 107 view(s) • June 17th, 2018, 00:52 MarkFL replied to a thread [SOLVED] 2.2.3 de with tan x in Differential Equations When you multiply by$\mu(x)$, you get: \sec(x)y'+\tan(x)\sex(x)y=\sec(x)\sin(2x) This can be written as: ... 8 replies | 107 view(s) • June 16th, 2018, 23:10 Thanks Steenis ... You have shown that$R^{(n)} / N \cong M$where$N = \text{ Ker } f$... ... ... ... ... (1) ... and we have by... 10 replies | 172 view(s) • June 16th, 2018, 19:51 MarkFL replied to a thread [SOLVED] 2.2.3 de with tan x in Differential Equations -\ln(\cos(x))=\ln\left((\cos(x))^{-1}\right)=\ln(\sec(x)) 8 replies | 107 view(s) • June 16th, 2018, 19:38 MarkFL replied to a thread [SOLVED] 2.2.3 de with tan x in Differential Equations \mu(x)=\exp\left(\int \tan(x)\,dx\right)=e^{\Large\ln(\sec(x))}=\sec(x) 8 replies | 107 view(s) • June 16th, 2018, 09:40 https://percentagecalculator.net/ "percent" means "per hundred" Simple example: 200 increases to 218: that's "9 per hundred", right?... 4 replies | 102 view(s) • June 16th, 2018, 00:29 300+300\cdot\frac{1666}{100}=300(1+16.66)=300\cdot17.66=5298 Here, we have taken 300, and added 1666% of 300 to it. However if we multiply 300 by... 4 replies | 102 view(s) • June 16th, 2018, 00:03 Thanks steenis ... but not sure if I follow .. ... but will try ... as follows ... We have an epimorphism$f:R^{(n)} \longrightarrow M$... 10 replies | 172 view(s) • June 15th, 2018, 16:28 \mu(x)=\exp\left(\int\frac{1}{x}\,dx\right)=e^{\ln(x)}=x 3 replies | 60 view(s) • June 15th, 2018, 15:53 We can see the integrating factor is$\mu(x)=x$and so the ODE will become: \frac{d}{dx}(xy)=x\sin(x) Upon integrating, we get: ... 3 replies | 60 view(s) • June 15th, 2018, 14:14 That's fine giving$x$as a function of$y$...I just chose to give$y$as a function of$x$since the original equation has$x$as the independent... 4 replies | 69 view(s) • June 15th, 2018, 12:44 We could also simply state: \d{x}{y}=e^y-x \d{x}{y}+x=e^y Now, our integrating factor is: \mu(y)=\exp\left(\int\,dy\right)=e^y 4 replies | 69 view(s) • June 15th, 2018, 03:08 I would begin here with the substitution: u=e^y\implies u'=uy' And so the ODE becomes: \frac{1}{u}u'=\frac{1}{u-x} Or: 4 replies | 69 view(s) More Activity ### 73 Visitor Messages 1. Welcome to the team of math helpers 2. Haha, that would be Mark. I like the way sounds, don't you? 3. Hey Balarka, As far as I'm concerned, you are welcome to post such information in any thread no matter how old it is. 4. Hey, way to go! 5. Hey Balarka, thanks, glad you are enjoying the challenge! As for the origin of this particular problem, I'm not sure, I found it in https://www.math.muni.cz/~bulik/vyuka/pen-20070711.pdf (page 67, no solutions) and thought it was interesting. It only says "Japan 1990" so I'm guessing it's from a contest of some sort, yes (the second part of the challenge is a custom addition of mine). Your proof appears to be correct although I will need some time to look at it in more detail. My solution approaches the problem in a similar way as yours, but proceeds somewhat differently, though I have not fully checked mine either (I will post it in a week as per the forum rules, as well as a reference solution if I can find one) 6. Done. Let me know if you need to edit more things in the future. 7. Hey Balarka, topsquark was purposely given a wrong number and he wanted me to spot for the error, which it turns out, I was wrong. I guess I just am not good at math. Hehehe... 8. You should be able to edit it now. Let me know if there is a problem. 9. Hm, I'm interested in sending you a private message. Can you open up one space ? 10. I haven't had time to play with it, but it *is* interesting. The failure of right-exactness is what interests me: I suspect this is akin to why in groups left-split implies right-split, but not vice versa. So I would be tempted to investigate what a sufficient condition on$G$would be so that the map:$Aut_N(G) \to Aut_N(H)$is onto. I feel the center of$G$will be relevant, here, so I would look at the two extremes:$G$abelian, and$G$with trivial center. I think outer automorphisms will be troublesome. On the other hand if$H$is an extension of$N$, and$G$is an extension of$H$, this might be fruitful (again, mimicking the field construction). For "concrete categories", for an object$A$we can always form the group$Aut(A)$of all isomorphisms$A \to A\$. I can't say right off-hand if we can do so for ANY category, but this might be true (if our category is a poset, the automorphism groups are all trivial). So "some" generalization is possible, I'm not sure "how wide".
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#### Basic Information

Date of Birth
January 12, 2000 (18)
Biography:
I know a thing or two about topology. Find number theory interesting but don't know much about it.
Location:
West Bengal, India
Interests:
Number Theory
Country Flag:
India

#### Signature

Some of my notes on number theoretic topics are on a few primality tests and on Hardy & Littlewood's result (incomplete). The other articles are on quintics : about a brief description of Kiepert algorithm and a short introduction on quintic-solving algorithms, respectively. I have also written up an introductory thread on Riemann Hypothesis

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MarkFL
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