Find the particular solution for this linear ODE :$y' '-2y'+5y=e^x \cos2x$.  How can I use Undetermined coefficients method ?
How do I find the particular solution of this second order inhomogenous differential equation? (Using undetermined coefficients).  $y''-4y'+5y = 4e^{2x} (\sin x)$  I can find the generel homogenous solutions but I need help for the particular.
I installed Windows 7 fresh and installed SP1. Now, when I try to check manually for Windows Updates it just hangs on the Checking for updates screen.    I tried running the tools in , but this did not fix the issue either:  No matter what I do it just hangs on the "Checking for updates..." screen and goes no further. Is there a law that you can add or multiply to both sides of an equation? Extra slash added to the chat room URLs in the side bar There is a extra slash added to the chat room URLs in the side bar. This is not causing any redirection issue or 404 not found error. Just observed it and want to notify to the development team about this. Seems it is not a bug, but that can . Currently the following URLs are binded against the chat rooms in the side bar.  Tavern on the Meta https://chat.meta.stackexchange.com//rooms/89  The Fire Department https://chat.meta.stackexchange.com//rooms/1181   GIF for the reference: Why does the Euclidean algorithm work for polynomials? What is the proof? Suppose I know that I can find the $\gcd$ of two integers with the Euclidean algorithm. What is the 'extension' so I can use this method also for polynomials?  Edit: I found an easy answer with less rigor which is approachable without knowledge of matrices:    also the first 3 subchapters of My tweets are not showing up in other people's mentions My replies are not showing up in other people's mentions. I tried tweeting several friends, my other accounts but my tweets just won't appear in their mentions? They do appear on my own Twitter page. It's been almost 24 hours now and it's pretty frustrating. Infinite algebraic extensions of $\mathbb{Q}$ I need help to solve the following exercise:   If $K$ is an algebraic extension of $\mathbb{Q}$ (finite or infinite), then we let $O_{K}$ denote the ring of algebraic integers in $K.$ If $\frak{P}$ is a prime ideal of $O_{K}$ then $\frak{P}∩\mathbb{Z}$ is a prime ideal of $\mathbb{Z}.$ Moreover, if $\frak{P}$ is non-zero, then so is $\frak{P}∩\mathbb{Z}$ . Thus $\frak{P}∩\mathbb{Z}=$$ p\mathbb{Z}$ for some prime $p.$ Show that $O_{K}/\frak{P}$  is a field, and is an algebraic extension of $\mathbb{F}_{p}$; then show that it is Galois over $\mathbb{F}_{p}$ with abelian Galois group.  Now suppose that $K/F$ is a (finite or infinite) Galois extension. Let $\frak{P},$  $O_{K}$ be as before and put $\frak{p}=\frak{P} \cap $$O_{F}$, a prime ideal of $O_{F}.$  Show that $\mathrm{Gal}(K/F)$ acts transitively on the set of prime ideals of $O_{K}$ above $\frak{p}.$   Thanks in advance Terminal, how to quit --More-- list How to change the "User License" type for customer portal users using a script? Glassware with scratched/etched surfaces generate more bubbles (, ). Why these rough surfaces allow easier heterogeneous nucleation? Comments are useful. Many, many posts need some small amount of meta discussion, and comments fulfill this need.   Comments are also noisy and distracting. Occasionally, someone will post an insightful and informative comment that complements the post its attached to... But more often, they're tangential, quickly irrelevant and in the way: stale comments show up first, making newer comments less visible.  The guidance here for a long time has been that comments are transient, . And yet, some do hang around for months or years because .   So let's fix that.   I propose that all comments older than 7 days be hidden by default unless the comment has been up-voted in the past 30 days. Hidden comments should be indicated by a note below the post ("add / show 3 more comments") and made visible to anyone who cares to click it.   This doesn't destroy anything, but it would get it out of the way of most readers - and hopefully encourage folks to edit it into the actual answers as a result.  Note: I previously suggested this . Other  have been . However, I'm not suggesting that comments be automatically deleted, and they should be hidden based purely on the age / activity of the comment itself, not of the post to which they're attached. When choosing cards for a deck, one of the most important things to consider is the number of land you put in. The biggest issue is mana curve, of course. What shortcuts are best for determining the proper amount of land with a given mana curve? Sorry if this is a stupid question, but I am mainly working with 5V PIC circuits and now want to integrate a component (nRF24l01+) that needs a 3.3V supply.  As I have a box full of ~7V wall-warts, I normally use a 7805 or similar LDO regulator to power the circuit. Now I want to also get 3.3V without using a separate external supply.  I'm looking for guidance on the "right" way to do this. I think the options are:   Use a voltage divider on the output of my 5V regulator to get 3.3V Use a 3.3V LDO regulator fed directly from the 7V wall-wart   Use the output of the 5V regulator as input to a 3.3V regulator   I can see that all of these would work (would they?) and that option 3 seems to waste least power, but I don't know what gotchas might arise by chaining two regulators like this.  What things do I need to consider when making this choice? Why is the edit button disabled? I edited some questions before, but now I get an error message when clicking the edit button. I thought there was a problem with the specific question, but I cannot click it on any question.  What's going on? umask in RHEL 6 How can one set the executable bit on files using umask? According to documentation, a umask of 000 should work, but in practice this only works on directories.  Also open to other methods of automatically setting +rwx on a particular user's created files if you have any. std::thread - "terminate called without an active exception", don't want to 'join' it What is the easiest way to update/upgrade an offline Ubuntu machine with the help of a Windows machine that has internet access?  This question also applies to installing new packages offline and not only updates/upgrades.  The Linux system shall remain completely cut off from the Windows machine, meaning there should be no ethernet connection or the likes between the two computers.  Update:  Please have patience, since I haven't updated this since two weeks. There are some complications getting apt-offline to work properly on Lubuntu and all other methods seem to be too old and deprecated:  AptOff - last update 2006 AptMedium - last update 2007 Keryx - last update 2011, looks like this project was discontinued  I hope I will be able to somehow update the offline machine, finally.  While I was still not able to update/upgrade the offline system due to authentication errors, I accepted an answer, because it's taking too long. Find executable files recursively I have got the directory called Test and a few directories inside it. Both Test and the directories inside it have executable files. I'd like to print them with ls. I'd use this command.  ls -l `find Test/ -perm /u=x,g=x,o=x -type f`   Is this a good/right/quick command or not?  My solution is:  find Test/ -executable -type f -exec ls -l {} \;   and got the same result as warl0ck and pradeepchhetri offered. Is there any matrix $2\times 2$ such that $A\neq I$ but $ A^3=I$? Is there any $2 \times 2$ matrix $A \neq I$ such that $A^3=I$?  In my opinion: no. Thank you very much. Filter bibliography by author? I would like to create a template for a publication list that can then be used by several people. The idea is that there is one bib-file which contains all of the publications. Peer-reviewed entries are marked with the keyword = pr. Then there is the master-file of the type scriptreport in which everyone can integrate their chapter-file in order to merge the publication lists of everybody into one file. The chapter file is the core of everything and should be reusable. It should filter out the entries for the respective author from the bib file and print them out in two lists (peer-reviewed and non-peer-reviewed). My problem is that I don't really know how to filter by author in this case. Here are the rough codes of the two files: Master: \documentclass[a4paper]{scrreprt}  \usepackage{biblatex}  \title{Publication list}  \addbibresource{sample.bib}  \begin{document}     \maketitle          \tableofcontents     \newpage          \include{Researcher}     \newpage \end{document}  chapter: \chapter*{Researcher} \addcontentsline{toc}{chapter}{Researcher}          \nocite{*}     \printbibliography[keyword={pr}, title={Peer-reviewed}]          \nocite{*}     \printbibliography[notkeyword={pr}, title={Non-peer-reviewed}] In Harry Potter, Who is Merlin? In Harry Potter, who is Merlin and what is his role in wizarding history?  His contribution to the wizarding history is apparently known from the fact that some special honors are named after him, such as the Order of Merlin (First Class, Second Class and so on...). Did he live around the time of the four founders of Hogwarts?