Solve the given differential equation.  $\frac{dy}{dx}=\frac{1}{xy(x^2 \sin y^2+1)}$  I have been trying to solve given differential equation using elementary approaches but no manipulation is a leading to a solvable form. Could someone help me with this?
Find the solution of following differential equation:     $$\frac{dy}{dx}=\frac{1}{xy(x^2 \sin (y^2)+1)}$$   Could someone hint me something to get through this problem?
Where in Europe can I purchase a car without residency? I am not a resident anywhere and plan to travel for the foreseeable future, mostly in Europe. My country has good visa-free access to most of Europe, so it is conceivable I could remain without any residency for quite some time.  I enjoy driving, and maintaining cars, and I would like to purchase a car somewhere in Europe.  Where, if anywhere, in Europe (or outside of Europe, but with the ability to drive the car in Europe) can I legally purchase and insure a car as a non-resident? I am open to creative solutions like setting up a company to own the car, if the capital and ongoing paperwork requirements for the company are not too onerous.    I am aware that I could save money, get places quicker, etc, by taking trains or flying. I have a passion for cars and driving. Suggesting that I not buy a car is out of scope of this question. I just finished backing up my system and when I try to upgrade to Utopic Unicorn, I get the error "Cannot Calculate the upgrades." I ran the upgrade by sudo apt-get dist-upgrade, sudo do-release-upgrade after the GUI method failed, they all gave the same error.  The feedback gives some recommendations:  This can be caused by:  * Upgrading to a pre-release version of Ubuntu  * Running the current pre-release version of Ubuntu  * Unofficial software packages not provided by Ubuntu    I am not upgrading to a pre-release version nor coming from one, I'm going from Ubuntu 14.04 LTS to 14.10. I have no broken packages and I have unchecked all my non-official software sources in the 'Software &amp; Updates' manager.  My guess left is the Unofficial software packages not provided by Ubuntu. If anyone could give any help as to how to check for unofficial packages using Synaptic or another, my appreciation.  Are there any other factors that may be causing this error and how would I go about checking/fixing those?  Thanks.  Edit: I have no broken or held packages. Everything is up-to-date, and restarting everything or anything has no effect. Who is the Community user? I see the  on the user page.  It seems to edit posts sometimes.  What is it? And why has it downvoted over 1800 times? See also: Bug Identification: Tiny Bugs I have seen these on my hands recently and I am wondering what they are. Urban Setting. South Central Pennsylvania. I must have a blind spot, but I cannot find what it is.   I made a small python script that removes VLC from the sound menu. It runs perfectly in any way I run it from the terminal or from a launcher or whatever you can think of.   What the script actually does is nothing more than get the get the current settings:  gsettings get com.canonical.indicator.sound interested-media-players   edit the list, and set the changed list by:  gsettings set com.canonical.indicator.sound interested-media-players "['newlist']"   These commands are executed by a python script,. However, when run from a cronjob (crontab -e) only the gsettings - get - part works, but not the gsettings - set - section. That the get section works fine with cron, I checked by making the script write data (the original as well as the edited) to an external file.  Not a python problem  To see if the problem is related to python code, I created a bash script that applies a changed sound menu items list. The story is the same: the bash script runs fine from the command line or a launcher, not from cron, while any other command in the same script would run fine. Also, if I add any command at the end of the script below, it works fine and it looks like the script is satisfied with its own work.  Why is the gsettings set command not working when initiated from cron?  This is the script:  #!/usr/bin/python3 import subprocess  def read_soundmenu():     # read the current launcher contents     get_menuitems = subprocess.Popen([         "gsettings", "get", "com.canonical.indicator.sound", "interested-media-players"         ], stdout=subprocess.PIPE)     return eval((get_menuitems.communicate()[0].decode("utf-8")))  def set_current_menu(current_list): # this takes no effect from cron     # preparing subprocess command string     current_list = str(current_list).replace(", ", ",")     subprocess.Popen([         "gsettings", "set", "com.canonical.indicator.sound", "interested-media-players",         current_list,         ])  current_list = read_soundmenu() for item in current_list:     if item == "vlc.desktop":         current_list.remove(item) set_current_menu(current_list) Does more reflective aluminum foil make a room cooler compared to less reflective foil? Aluminum foil is said to be not absorbing light at all. It reflects light. So, does it mean that a more shiny aluminum foil will reflect more light and thus make the room more cooler as compared to less shiny foil?  If yes, then where does unreflected light go in case of less shiny aluminum foil?  Does less shiny and more shiny actually make a difference? Why?  In order to keep whole room cool will it help if I stick the foil to the outside of wooden door (exposed to the sunlight) too? Let $(a_n)_{n \in \mathbb{N}}$ be a convergent sequence with limit $a \in \mathbb{R}$. Show that the arithmetic mean given by: $$s_n:= \frac{1}{n}\sum_{i=1}^n a_i \tag{A.M.} $$ also converges to $a$.  I have read:  but unfortunately the answers there don't help me much because I don't understand their substitutions and most of it all, why their substitutions seem to work.   What I know from the problem is that since $a_n$ is convergent and $\epsilon &gt;0$ is given, I can say that:   $$\exists N_1 \in \mathbb{N}, \forall n \geq N_1: |a_n-a|&lt;\epsilon_1 $$ I also know that since $a_n$ is convergent, it is bound, so $(a_n) &lt; M, \ \forall n \in \mathbb{N}$   I need to show that: $$\exists N_2 \in \mathbb{N}, \forall n \geq N_2: |s_n-a|&lt; \epsilon_2$$ I started as follows: $$ \left|s_n-a \right| = \left|\frac{1}{n}\sum_{i=1}^na_i -a\right|= \left|\frac{1}{n}\sum_{i=1}^m(a_i-a)+\frac{1}{n}\sum_{i=m+1}^n(a_i-a) \right| \\ \leq \frac{1}{n} \sum_{i=1}^m|(a_i-a)|+\frac{1}{n}\sum_{i=m+1}^n|a_i-a|$$ I believe to understand that the left sum after the $\leq$ is finite, bound and doesn't depend on the values that $n$ takes on. However, I don't understand where all the substitutions come from and make this proof so seemingly easy to complete.   Is there a general idea I can follow to complete such proofs? Because I know that the last step is to show that the given sum is smaller than $\epsilon$. I also know that I should bring the condition $a_n &lt; M$ into place somewhere, but I don't know where.  If I choose an $n \geq N: |a_n-a|&lt; \epsilon'$ what does that tell me about $|a_i-a|$? I know that they are seemingly the same just with a different index. Properties possessed by $H , G/H$ but not G i) Does there exist a group $G$ with a normal subgroup $H$ such that $H , G/H$ are abelian but $G$ is not ?   ii) Does there exist a group $G$ with a normal subgroup $H$ such that $H , G/H$ are cyclic but $G$ is not ? How best to include other scripts? How can I get this symbol without using bbold? A solution I saw somewhere suggested to use   \usepackage{bbold} $\mathbb{1}$   which works well and I get what I want. However, now other symbols used to represent real numbers, natural numbers, etc look ugly.    I'd like them to look (without using bbold)    I'd like to only use that package to achieve that strange double one. Is there any way I can do that? What is the difference between "Redirection" and "Pipe"? This question may sound a bit stupid, but I can not really see the difference between redirection and pipes.  Redirection is used to redirect the stdout/stdin/stderr, e.g. ls &gt; log.txt.  Pipes are used to give the output of a command as input to another command, e.g. ls | grep file.txt.  But why are there two operators for the same thing?  Why not just write ls &gt; grep to pass the output through, isn't this just a kind of redirection also? What I am missing? How to test whether a file uses CRLF or LF without modifying it? I need to periodically run a command that ensures that some text files are kept in Linux mode. Unfortunately dos2unix always modifies the file, which would mess file's and folder's timestamps and cause unnecessary writes.   The script I write is in Bash, so  I'd prefer answers based on Bash. How to test if a player is near coordinates in 1.13? What is the difference between encrypting some data vs signing some data (using RSA)?    Does it simply reverse the role of the public-private keys?    For example, I want to use my private key to generate messages so only I can possibly be the sender.  I want my public key to be used to read the messages and I do not care who reads them.  I want to be able to encrypt certain information and use it as a product-key for my software.  I only care that I am the only one who can generate these.  I would like to include my public key in my software to decrypt/read the signature of the key.  I do not care who can read the data in the key, I only care that I am the only verifiable one who can generate them.  Is signing useful in this scenario? MCMC in a frequentist setting I have been trying to get a sense of the different problems in frequentist settings where MCMC is used. I am familiar that MCMC (or Monte Carlo) is used in fitting GLMMs and in maybe Monte Carlo EM algorithms. Are there more frequentist problems where MCMC is used? Post hoc test after ANOVA with repeated measures using R What, exactly, is transferred along supply lines? How do I start applications automatically on login? How can I make an application automatically start when I have logged in? Why didn't Kenobi start training Luke earlier? When Anakin was only 9 years old, everyone in the Jedi Council was arguing that he was already too old for Jedi training.  When it comes to Luke, it was a pre-planned agenda to make him a powerful Jedi. So, why did Kenobi wait for Luke to be much older? He could have started Luke's training by himself. Retrieving minimum width that contains specified fraction of all values I'd like to find the min/max boundaries of a sliding window of minimum size that contains a certain fraction of the total number of elements in an array or collection of numbers.   Example: taking integers to make it easier to explain, say the proportion of elements that we're looking for is 50% on this array:  [1,1,2,3,3,3,3,3,3,4,5,6,7,8,9,10]  The mystery function would return something like ( 2, 4 ), meaning that the minimum value is 2 and the max value is 4 (let's assume it's inclusive and note that these are VALUES, not indices). That little window contains 8 of the 16 values and it's only 2 units wide, the narrowest such window that contains half the number of values.  Note: the quartiles are [1,1,2,3], [3,3,3,3], [3,4,5,6], [7,8,9,10] so they are NOT what I'm looking for.  I can code it...may take some time to get it nice. Hopefully somebody has run across it before. Does it have a name?  Is there an existing method that somebody knows about?  I am interested in Python implementations.   UPDATE:  Thanks to Glen_b who gave the names 'short-half' and 'shortest interval' I was able to come up with this: