I would like to solve:  $$\dot{y} = -\frac{2y(t)}{5t} +\frac{3}{5y(t)^4} $$  I was given a hint to use the transformation.  $$ z(t) = t^\alpha y(t)$$ where $\alpha \in \mathbb{R}$. I've seen this been done before but it seems like you just guess the solution. Is there a way to go about this?
Consider equations defined in $D_x = (0,\infty) \times (0,\infty)$  1) Find the maximal solution to  $$ \dot y = \frac{3t^2}{5y^4} $$ satisfying the initial value problem $y(1) = 2^{\frac{1}{5}}$  I have found the maximum solution to be $((0,\infty), (t^3+1)^\frac{1}{5})$  2) Find the maximal solution to   $$ \dot y = -\frac{2y}{5t}+\frac{3}{5y^4}$$  satisfying the IVP $y(1) = 2^{\frac{1}{5}}$.  (HINT: Use a transformation of the form $t^{\alpha}y(t)$.   I hope someone can explain how to use the transformation to find the maximal solution.
We just bought a Lenovo  (which is supposed to have the Intel 8265 for wireless). This laptop was bought in part because it is certified to run Ubuntu and as such to me at least it would make sense for things to work out of the box... but no such luck.  First, I installed Ubuntu 17.10 and after installation realised Wi-Fi was not working. I also tried Ubuntu 16.04 from a USB drive since that is the version of Ubuntu it is certified for, but no luck there either.  The wireless chip is not detected by lshw (or even lspci by the looks of it), ip link does not show a wireless interface, and the iwlwifi kernel module is not loaded at boot (I can load this myself using modprobe iwlwifi but this does not make Wi-Fi work). I think it is a combined Wi-Fi/Bluetooth chip, and Bluetooth does appear to work (or at least Bluetooth shows up in Gnome and rfkill list).  modinfo iwlwifi | grep 8265 shows me a file ending in -34 is supposedly loaded but only a file ending in -33 (and some other lower numbers) is present in /lib/firmware, if that helps).  I have also installed the Linux 4.14.9 kernel in an attempt to get things to work, but this did not resolve the issue either.  Further information  root@ThinkPad-E570:~# modinfo iwlwifi | grep 8265 firmware:       iwlwifi-8265-34.ucode root@ThinkPad-E570:~# rfkill list all 0: tpacpi_bluetooth_sw: Bluetooth     Soft blocked: no     Hard blocked: no 1: hci0: Bluetooth     Soft blocked: no     Hard blocked: no root@ThinkPad-E570:~# dmesg | grep iwl root@ThinkPad-E570:~# lspci -nnk | grep 0280 -A3 05:00.0 Network controller [0280]: Realtek Semiconductor Co., Ltd. Device [10ec:c821]     Subsystem: Lenovo Device [17aa:c024]   Update  I just noticed that the laptop does not have an Intel wireless chip at all, but in fact has a Realtek one... which means that the  of the shop I bought this laptop at were not accurate... Sigh. Same problem stands, however, just with a crappier wireless chip. Why doesn't the Related question list show that questions are closed? I saw a question on Meta that was obviously going to be a duplicate:        And indeed, looking at the "Related" questions list for that question showed a number of duplicates:    Being the good citizen I am, I tried to vote to close (technically Flag as duplicate as I've not got the rep here to vote to close) it as an Exact Duplicate only to find myself falling into a rabbit hole of Closed, Duplicate questions. Is there any way to flag a closed question as such in the Related list?  Mostly because the first one I picked was closed as a duplicate of the second one, which was closed as a duplicate of the one that is now listed as the duplicate/linked answer.   Edit to respond to comment:  I take the point about "not voting to close on title alone", and normally wouldn't, however as the questions had identical titles, and it's pretty clear what they should be asking, I clicked the first one:    which lead to:  which leads to:  - but I'd got bored following links and didn't check that one as the first two were identical, so assumed this was too and didn't want to see how deep the rabbit hole led.   In the related list, there's only one other question in there that is an exact duplicate, but hasn't (currently) been closed as such which is:      Reasoning for highlighting closed questions:  The "Questions with similar titles" does display the closed titles when asking the question, so it should be fairly possible to include.  If there are clearly duplicate titles, then as a reader/reviewer would be helpful to know which ones are already closed as duplicates so you can either:   Use the remaining open questions to focus on which of those is the canonical answer to close this with. Use the closed questions to find the canonical answer (which failed for me with my route of clicks). So we learned telescoping series in class and I came across this question in my textbook and I tried to evaluate it, but I don't understand how to do it.   $$ \sum\limits_{k=1}^n\left(k \cdot k!\right) $$  According to the answers:  $$ \sum\limits_{k=1}^n\left(k \cdot k!\right) = (n+1)! - 1 $$  We learned how to simplify certain telescoping series using partial fractions but I don't have any idea on how to start this question. I am trying to convince my friend that the integral of $0$ is $C$, where $C$ is an arbitrary constant. He can't seem to grasp this concept. Can you guys help me out here? He keeps saying it is $0$. I have an ArrayList&lt;String&gt;, and I want to remove repeated strings from it. How can I do this? I'm an on and off user of LaTeX so I'm not familiar with every package out there. Having said that, whenever I use LaTeX and need to accomplish a certain goal (i.e. ), I search around and find some kind of solution that involves a package that I didn't know about. I think that's great, I learn something new, and it goes in my template file.  Every now and then, though, my search comes up with a package that, after much wrangling, I find out that it's obsolete. An example of this is just recently I came across the subfigure package and wanted to try it out. Soon after I found out from here that it has become . I usually keep my TeX up-to-date because I like keeping up with new XeLaTeX features.   My question is, is there a map or timeline of what TeX packages should be avoided because there are better ways of doing things? An idea I have is some kind of list of all packages split by what they accomplish, then cancelling out packages whose features are incorporated into and improved upon by newer packages.  Edit: another example is lscape versus pdflscape. The latter implements rotating pages in the final PDF not just for pdftex but also for other drivers such as xetex. The only way I found out about this was Googling latex lscape rotate xelatex, for which the second link leads to the  (PDF).  Great answers so far. I'll check them out and see which one works best for me.  Edit 2: Turns out that my question is a bit of a dupe in the sense that a great answer came up on an unrelated question. The nag package . Gotta try it! My PC has a build-in VT1828S chip. The connection between PC and monitor (which has built-in speakers) is through an HDMI cable.  Audio preferences shows 2 devices for audio output: analog stereo and RS880 Audio Device [Radeon HD 4200] digital stereo (HDMI).  When I plug a headphone in the rear jack and I choose the former device, everything works. When I choose the latter device, instead, no sound is heard, and video playback is too fast. It is as if video frames want to synchronise with the audio timing, but the audio timing information is wrong.  HDMI audio worked perfectly with Ubuntu 11.04, but stopped after 11.10 upgrade. Regarding the recalc in question rep increase what happens due to the cap? Include prior knowledge in regression model I've a classical dataset with real attributes and I want to perform a regression.  But, not all the entries in the training dataset are trustworthy; there is an attribute that I can turn into a confidence value (between 0 and 1) to say how much I can trust the label value. For example, if the confidence value is 0, I mustn't take the entry into consideration.  Is there a way to do this? How to model the curly cable part of the phone Hello. I am a beginner in Blender. I started modeling this phone and when I got to the curly cable part it was a real challenge. Could someone guide me on this. How can I better optimize my tables and a LEFT JOIN query to find items that don't yet exist in the right table? I have two tables that represent a list of urls and their related word indexes. Here are the table definitions for reference.  desc urllist; +-------+---------------------+------+-----+---------+----------------+ | Field | Type                | Null | Key | Default | Extra          | +-------+---------------------+------+-----+---------+----------------+ | id    | bigint(20) unsigned | NO   | PRI | NULL    | auto_increment | | url   | text                | NO   |     | NULL    |                | +-------+---------------------+------+-----+---------+----------------+   and  desc wordlocation; +----------+---------------------+------+-----+---------+-------+ | Field    | Type                | Null | Key | Default | Extra | +----------+---------------------+------+-----+---------+-------+ | urlid    | bigint(20) unsigned | NO   |     | NULL    |       | | wordid   | bigint(20) unsigned | NO   |     | NULL    |       | | location | int(10) unsigned    | NO   |     | NULL    |       | +----------+---------------------+------+-----+---------+-------+   The software app is a web spider. It crawls a list of urls, extracts those urls, and inserts these into the urllist table. Then, an indexer checks to see what urls have not yet been indexed, and then proceeds to index said urls.  Here is the query I am using to find items in the left table (urllist) that have not yet been indexed in the right table (wordlocation). This query is as suggested on the :  select * from urllist ul  left join wordlocation wl on ul.id = wl.urlid  where wl.urlid IS NULL;   As of this writing my test database has only 600 indexed urls, and the wordlocation table has 1.3 million rows.  However, my CPU is at 100%, and the longest I've waited to see if the query would complete is a half hour (which, it never did by the way).  To be thorough, here is the explanation of the query:  explain select * from urllist ul left join wordlocation wl on ul.id = wl.urlid where wl.urlid IS NULL; +----+-------------+-------+------+---------------+------+---------+------+---------+-------------------------+ | id | select_type | table | type | possible_keys | key  | key_len | ref  | rows    | Extra                   | +----+-------------+-------+------+---------------+------+---------+------+---------+-------------------------+ |  1 | SIMPLE      | ul    | ALL  | NULL          | NULL | NULL    | NULL |   50364 |                         | |  1 | SIMPLE      | wl    | ALL  | NULL          | NULL | NULL    | NULL | 1351371 | Using where; Not exists | +----+-------------+-------+------+---------------+------+---------+------+---------+-------------------------+   I need this query to finish in seconds, not minutes. Also, I'm worried about scalability. I have 40,000 unique urls that are waiting to be added to the index, so how do I take that into consideration with my table and query design? 400,000 urls?  Just a couple notes about my decisions on the current table structure.  I have no intention of stopping at 400,000 urls, but perhaps bigint(20) is a bit overzealous?   Url as text is for more practical reasons. I index a lot of Asian and other foreign language domains which do not appear as their equivalent Kanji or other characters in the database and frequently take more than 255 characters.  I'm using MySQL. I'm definitely open to suggestions as to better table and query design. Please let me know if I can provide more information. Can I travel to Schengen countries that were not on my itinerary when I applied? Is it possible to combine processing power of 2 computers? I compile my project with VIsual Studio 2005 Express Edition, and get this linking error. Can anyone suggest how to solve that? Get the client IP address using PHP Find My iPhone Email Notification Is the email notification from Apple that your device has been tracked using Find My iPhone a new feature? Determine all $f : \mathbb R \rightarrow \mathbb R$ such that $f(f(x) + y) = f(x^2 - y) + 4yf(x)$. Determine all $f : \mathbb R \rightarrow \mathbb R$ such that $$f\big(f(x) + y\big) = f(x^2 - y) + 4yf(x)$$ for all $x,y\in\mathbb{R}$.   $f(x) = 0$ is obvious , but how can we find all other functions?  Thanks in advance! How to tail multiple files using tail -0f in Linux/AIX Why isn't  generic?    Seems like Collection&lt;E&gt; could have boolean remove(E o);   Then, when you accidentally try to remove (for example) Set&lt;String&gt; instead of each individual String from a Collection&lt;String&gt;, it would be a compile time error instead of a debugging problem later. Visa for transit in Seoul