I'm working on solving this inhomogeneous problem with the method of undetermined coefficients using tips from this website: . There is an equation halfway down that looks almost exactly the same as mine, so I referenced it for help, but I'm still not getting the right answer. The equation is this: $$y''-2y'+y=te^t$$ I started out with my "guess" equation as: $Y_P(t)=e^t(At+B)$  Then I took the first and second derivatives: $$Y_P'(t)=e^tAt+Be^t+Ae^t$$ $$Y_P''(t)=e^tAt+2Ae^t+Be^t$$  After finding that I plugged in the three equations to the LHS of the original equation and then separated like terms:  $$e^tt(A-2A+A)+e^t(2A+B-2A-2B+B)=te^t$$ In each of the parentheses I end up with a value of $0$, which can't be right. What am I doing wrong?
In order to solve  $$y''-2y'+y=te^t$$ I did:  $$y = (at+b)e^t\implies\\ y' = ate^t+ae^t+be^t\implies \\y''= ate^t+2ae^t+be^t$$  but when I put these in the differential equation I'm getting zeros eveywhere. Does somebody know what I'm doing wrong?
Finding an Inverse Function and Composition of Functions? You can reach this IP address  (if my computer is online). I want to assign a domain to it so I wonder how is that possible when I have no DNS? I do own my domain which is ".com". My IP is static.  Thanks I have a geotiff raster image that has a coordinate system with longitudes from 0 to 360. The horizontal center of the image is 180 longitude. See image below:    I want to transform it to EPSG:4326 SRS with -180 180 longtitude range.  And I want the center of the image to be at Greenwich meridian (0). I guess this srs is very widely used. I expect the result look like this:    So I use a gdalwarp command to reproject:  gdalwarp -s_srs '+proj=latlong +datum=WGS84 +pm=180dW' -t_srs EPSG:4326 test_col.tif test_4326.tif   But I only get a tiff with bigger dimensions (more pixels) and EPSG:4326 metadata. The image itself looks the same, as the initial one. But I expect it to swap the hemispheres.  How do I gdalwarp an image to be strictly -180 180 EPSG:4326 with the center in 0 longitude?  This is gdalinfo of my initial file:  Origin = (-0.102272598067084,89.946211604095552) Pixel Size = (0.204545196134167,-0.204423208191126) Metadata:   AREA_OR_POINT=Area Image Structure Metadata:   INTERLEAVE=BAND Corner Coordinates: Upper Left  (  -0.1022726,  89.9462116) (  0d 6' 8.18"W, 89d56'46.36"N) Lower Left  (  -0.1022726, -89.9462116) (  0d 6' 8.18"W, 89d56'46.36"S) Upper Right (     359.897,      89.946) (359d53'50.18"E, 89d56'46.36"N) Lower Right (     359.897,     -89.946) (359d53'50.18"E, 89d56'46.36"S) Center      ( 179.8975000,  -0.0000000) (179d53'51.00"E,  0d 0' 0.00"S)   This is gdalinfo after gdalwarp     Origin = (-180.102727401932952,89.946211604095552) Pixel Size = (0.091397622896436,-0.091420837939082) Metadata:   AREA_OR_POINT=Area Image Structure Metadata:   INTERLEAVE=PIXEL Corner Coordinates: Upper Left  (-180.1027274,  89.9462116) (180d 6' 9.82"W, 89d56'46.36"N) Lower Left  (-180.1027274, -89.9699975) (180d 6' 9.82"W, 89d58'11.99"S) Upper Right ( 179.8211116,  89.9462116) (179d49'16.00"E, 89d56'46.36"N) Lower Right ( 179.8211116, -89.9699975) (179d49'16.00"E, 89d58'11.99"S) Center      (  -0.1408079,  -0.0118929) (  0d 8'26.91"W,  0d 0'42.81"S) Evaluate $\int_0^{\infty}\frac{\log x}{1+e^x}\,dx$ Extending from two classes Can a virtualized machine have the CPU and RAM resources of multiple underlying physical machines? Penguin Brainteaser : 321-avoiding permutations There are $k$ penguins, $k\ge 3$. They are all different heights. How many ways are there to order the penguins in a line, left to right, so that we cannot find any three that are arranged tallest to shortest (in left to right order)? The penguin triples do not have have to be adjacent.  This problem is courtesy of someone I know only as "DaMancha." Etymology of "history" and why the "hi-" prefix? According to , history comes from the same root as story. If they are from the same word, where does hi- come from? Is it just because of the English habit of taking names from other languages verbatim or is there something more to it? Possible Duplicate:          We have some "theme colors" that are reused in our CSS sheet.  Is there a way to set a variable and then reuse it?  E.g.  .css OurColor: Blue  H1 {   color:OurColor; } How can I dynamically unload a javascript file? How well will WCF scale to a large number of client users? Does anyone have any experience with how well web services build with Microsoft's WCF will scale to a large number of users?  The level I'm thinking of is in the region of 1000+ client users connecting to a collection of WCF services providing the business logic for our application, and these talking to a database - similar to a traditional 3-tier architecture.   Are there any particular gotchas that have slowed down performance, or any design lessons learnt that have enabled this level of scalability? Loading D3.js data from a simple JSON string I always thought water sources were called taps in kitchens, bathrooms etc, but a Google search only returned outdoor taps.  So my question is, what are indoor taps really called? Like this one: Combinatorial argument to prove the recurrence relation for number of derangements Give a combinatorial argument to prove that the number of derangements satisfies the following relation: $$d_n = (n − 1)(d_{n−1} + d_{n−2})$$ for $n \geq 2$.  I am able to prove this algebraically but not able to see the combinatorial example. I am trying to automate these steps so that I don't need to do this on every machines manually. I need to install latest app server software (abc.tar.gz) on all the unix boxes.  I need to do this in around 12 machines - "machine1" ... "machine12". I have a master machine "machine0" which has abc.tar.gz file so I was thinking to run my script from this machine only and install abc.tar.gz software by following below steps in all those 12 machines one by one. My unix account id is david and my process runs as golden user.  This is the steps I follow if I am installing abc.tar.gz in "machine1":  david@machine1:~$ sudo scp david@machine0:/home/david/abc.tar.gz . david@machine1:~$ sudo stop test_server david@machine1:~$ sudo su - golden golden@machine1:~$ cd /opt/process golden@machine1:/opt/process$ rm -rf * golden@machine1:/opt/process$ exit david@machine1:~$ sudo cp abc.tar.gz /opt/process david@machine1:~$ sudo chown -R golden /opt/process david@machine1:~$ sudo su - golden golden@machine1:~$ cd /opt/process golden@machine1:/opt/process$ tar -xvzf abc.tar.gz golden@machine1:/opt/process$ exit david@machine1:~$ sudo start test_server   How can I automate this so that it can do the same steps in all 12 machines one bye one? I mean install abc.tar.gz in machine1 first, then install on machine2 and go on..  I want to run this script from machine0 only.  Is there any way to automate this? How do I use sudo to redirect output to a location I don't have permission to write to? I've been given sudo access on one of our development RedHat linux boxes, and I seem to find myself quite often needing to redirect output to a location I don't normally have write access to.  The trouble is, this contrived example doesn't work:  sudo ls -hal /root/ &gt; /root/test.out   I just receive the response:  -bash: /root/test.out: Permission denied   How can I get this to work? Package Cache File corrupted From advice on  , I've opened a new question about the same issue, as it turned out my problem was not the one described in the question, information I did not know at the time. I'm running Ubuntu 16.04.  $ sudo apt-get update  Hit:1 http://archive.ubuntu.com/ubuntu xenial InRelease Get:2 http://archive.ubuntu.com/ubuntu xenial-updates InRelease [102 kB] Get:3 http://archive.ubuntu.com/ubuntu xenial-backports InRelease [102 kB] Get:4 http://archive.ubuntu.com/ubuntu xenial-security InRelease [102 kB] Get:5 http://archive.ubuntu.com/ubuntu xenial-updates/main amd64 DEP-11 Metadata [307 kB] Get:6 http://archive.ubuntu.com/ubuntu xenial-updates/main DEP-11 64x64 Icons [226 kB] Get:7 http://archive.ubuntu.com/ubuntu xenial-updates/universe amd64 DEP-11 Metadata [185 kB] Get:8 http://archive.ubuntu.com/ubuntu xenial-updates/universe DEP-11 64x64 Icons [268 kB] Get:9 http://archive.ubuntu.com/ubuntu xenial-updates/multiverse amd64 DEP-11 Metadata [5,888 B] Get:10 http://archive.ubuntu.com/ubuntu xenial-backports/main amd64 DEP-11 Metadata [3,324 B] Get:11 http://archive.ubuntu.com/ubuntu xenial-backports/universe amd64 DEP-11 Metadata [4,712 B] Get:12 http://archive.ubuntu.com/ubuntu xenial-security/main amd64 DEP-11 Metadata [62.7 kB] Get:13 http://archive.ubuntu.com/ubuntu xenial-security/main DEP-11 64x64 Icons [71.2 kB] Get:14 http://archive.ubuntu.com/ubuntu xenial-security/universe amd64 DEP-11 Metadata [51.3 kB] Get:15 http://archive.ubuntu.com/ubuntu xenial-security/universe DEP-11 64x64 Icons [85.1 kB] Fetched 1,578 kB in 1s (1,529 kB/s)                                     Reading package lists... Error! E: Read error - read (5: Input/output error) W: You may want to run apt-get update to correct these problems E: The package cache file is corrupted   If there's any more information you need, don't hesitate to ask in the comments.  Edit 1:  $ sudo df -h Filesystem      Size  Used Avail Use% Mounted on udev            5.9G     0  5.9G   0% /dev tmpfs           1.2G  9.4M  1.2G   1% /run /dev/sda1       135G  7.2G  121G   6% / tmpfs           5.9G   14M  5.9G   1% /dev/shm tmpfs           5.0M  4.0K  5.0M   1% /run/lock tmpfs           5.9G     0  5.9G   0% /sys/fs/cgroup tmpfs           1.2G   88K  1.2G   1% /run/user/1000 /dev/sdb1       932G  300G  633G  33% /media/adoria298/MDrive1   Edit 2 SMART Test results: Why do the Localization of a Ring This question may be a bit vague, but neverthless, i would like to see an answer. Wikipedia tells me that:   In abstract algebra, localization is a systematic method of adding multiplicative inverses to a ring.   It is clear that for integral domains, we have the Field of Fractions, and we work on it. It's obvious that a Field has multiplicative inverses. Now if we consider any arbitrary ring $R$, by the definition of localization, it means that we are adding multiplicative inverses to $R$ thereby wanting $R$ to be a division ring or a field. My question, why is it so important to look at this concept of Localization. Or how would the theory look like if we never had the concept of Localization. Proof: in $\mathbb{R}$, $((0,1),|\cdot|)$ is not compact. Let $(M,d)$ be a metric space, and $A\subset M$. By definition, $A$ is said to be compact if every open cover of $A$ contains a finite subcover.  What is wrong with saying that, in $\mathbb{R}$, if $I=(0,1)$, we can choose $G=\{(0,\frac{3}{4}), (\frac{1}{4}, 1)\}$, which satisfies $I \subset \bigcup_{U\in G} U$, but we can't extract a finite subcover, so $I$ is not compact. Is $G$ a finite subcover of $G$, so it is not a valid cover for proving this? I would take $\cup_{n\in\mathbb{N}} (\frac{1}{n},1)$ in order to prove this, can we conclude that every open cover is necessarily a infinite union of open sets $\neq \emptyset$? LaTeX seems to be having problems handling nested optional arguments. I've included a minimal code example that generates the error:  \documentclass[12pt,oneside]{book} \begin{document}  \newcommand{\termbad}[2][]{#2#1} \newcommand{\termgood}[2][]{#2#1}  \newcommand{\up}[1]{#1} \newcommand{\dd}[1][]{#1}  \termgood{\up{Tart}}{Pop} \termbad[\up{Tart}]{Pop}      \termgood{\dd[Tart]}{Pop} \termbad[{\dd[Tart]}]{Pop} %\termbad[\dd[Tart]]{Pop}   \end{document}   If you run this code, it works. If you remove the % in the second to last line, it fails with:  Runaway argument?  Tart{Pop} \par \par \end {document}  !File ended while scanning use of \dd.   After further tinkering, I have discovered the problem: LaTeX is reading the ] for the inner optional argument as the end of the outer optional argument and then passing a malformed argument in. So it is passing in \dd[Tart as the optional argument to \termbad instead of \dd[Tart].  This still feels like a bug to me. Nesting braces in arguments works, brackets should as well. The following are workarounds:   Enclose the inner optional argument in braces (as in the line before %). Redefine your inner function to require its argument instead of using optional arguments. Redefine your outer function to require its argument instead of using optional arguments.   Any one of the three works around the issue.  (Reposted here; question was originally posted to stackexchange and then closed instead of being migrated.)