This equation $(x^3+xy^2−y)dx+(y^3+x^2y+x)dy=0 $ is Integration factor found by inspection. The answer on the book is $2\arctan(\frac{y}{x})=c-x^2-y^2$
$(x^3+xy^2-y)dx+(y^3+x^2y+x)dy=0$ I tried to find on Wolfram Alpha but it showed only the solution not in step-by-step, I know that the factor is $\frac{1}{x^2+y^2}$ but how to find it?
How to sort a character vector where elements contain letters and numbers in R? Determining a tricky limit What is the limit of   $$\lim_{n \to \infty} \frac{\log n}{n^\delta}$$  where $\delta &gt; 0$? How do I deal with 'sudoers.so must be only be writable by owner'? Whenever I try to install or remove something using terminal it gives the following error message:  bluebird@bluebird:~$ sudo apt-get update sudo: /usr/lib/sudo/sudoers.so must be only be writable by owner sudo: fatal error, unable to load plugins bluebird@bluebird:~$ sudo apt-get remove vlc sudo: /usr/lib/sudo/sudoers.so must be only be writable by owner sudo: fatal error, unable to load plugins bluebird@bluebird:~$ sudo apt-get install apt-file sudo: /usr/lib/sudo/sudoers.so must be only be writable by owner sudo: fatal error, unable to load plugins Suppose $\{a_n\}$ is a sequence such that the subsequences $\{a_{2n−1}\}$ and $\{a_{2n}\}$ converge to the same limit, say $a$. Show that $\{a_n\}$ also converges to $a$. Is there any actual written dialog for the astromech droids? When R2-D2 and BB-8 converse in The Force Awakens for example, is there any written record of what the two characters were saying to each other?  I mean actual dialog, if it exists, and not something like ”BB-8 beeps excitedly”. Do you have to take the second leg of a domestic flight? Show that the set of all polynomials whose constant term is a multiple of 3 is an ideal of the ring $Z[x]$.   Attempt: Suppose then we need to show   if $p(x), q(x) \in I$ then $p(x) + q(x) \in I$  and if $r(x) \in Z[x]$ , then $p(x)r(x) \in I$ and $r(x)p(x) \in I$.  And $0 \in Z$, then $0 \in I$.  Then let   $I =$ {$a_nx^n + a_{n-1}x^{n-1} + ...+a_1x + a_0$ | $a_i \in Z$, $a_0\in 3Z$}  $p(x)  = a_nx^n + a_{n-1}x^{n-1} + ...+a_1x + 3a$  and $q(x) = b_mx^n + b_{m-1}x^{n-1} + ...+b_1x + 3b$  Here we do not assume that $p(x) $ and $q(x)$ have the same degree.  Then $p(x) + q(x)  = [a_nx^n + a_{n-1}x^{n-1} + ...+a_1x + 3a]  +  [b_mx^n + b_{m-1}x^{n-1} + ...+b_1x + 3b] = 3(a + b) + (a_1 + b_1)x + ....+ (a_n + b_m)x^n$.  so $p(x) + q(x) \in I$  And $0 \in Z$ is also in $I$, since for $p(x) = 0x^n + ....+ 3(0) = 0$.  And let $r(x)= c_nx^n + ...+3c  \in Z[x] $.  Then $r(x)p(x) = 3(3ac) + (3b_1 + 3a_1) + ....+ a_nb_mx^{2n}$  So $r(x)p(x) \in I$.  Can someone please help? I am not really sure how to prove this. I am getting confused with the underscrips Any help or better approach would really help. Thanks in advance! Best resources to learn bash scripting? url completion in cartoDB info windows Pending suggested edit message bug I just tried to edit a post on Stack Overflow but when I pressed the 'edit' button it showed me this message on a white page.    I know what the message means but I don't think it is supposed to show up in a white page. So, is this a bug or is it something else? GRUB doesn't show Windows 10 Whenever I boot into my system, Linux directly boots. If I press shift, GRUB shows only Linux, not Windows. Here are results of fdisk and update-grub. I think I have installed Linux the wrong way.  $ fdisk WARNING: GPT (GUID Partition Table) detected on '/dev/sda'! The util fdisk doesn't support GPT. Use GNU Parted.   Disk /dev/sda: 1000.2 GB, 1000204886016 bytes 255 heads, 63 sectors/track, 121601 cylinders, total 1953525168 sectors Units = sectors of 1 * 512 = 512 bytes Sector size (logical/physical): 512 bytes / 4096 bytes I/O size (minimum/optimal): 4096 bytes / 4096 bytes Disk identifier: 0x00000000     Device Boot      Start         End      Blocks   Id  System /dev/sda1               1  1953525167   976762583+  ee  GPT Partition 1 does not start on physical sector boundary.  $ update-grub Generating grub configuration file ... Warning: Setting GRUB_TIMEOUT to a non-zero value when GRUB_HIDDEN_TIMEOUT is set is no longer supported. Found linux image: /boot/vmlinuz-3.19.0-32-generic Found initrd image: /boot/initrd.img-3.19.0-32-generic Found memtest86+ image: /boot/memtest86+.elf Found memtest86+ image: /boot/memtest86+.bin   No volume groups found done Correct use of will & would? What would be the correct use of will &amp; would in these sentences?  1) What will happen if I say to my boss that I will not come tomorrow?  2) What will happen if I would say to my boss that I will not come tomorrow?  3) What will happen if I will say to my boss that I will not come tomorrow?  4) What would happen if I would say to my boss that I will not come tomorrow?  There are four sentences which one should I use and in which situation? Prove $\sqrt{2} + \sqrt{5}$ is irrational How to remove enamel from wire? I want to repair my computer mouse cable which has become disconnected from the PCB. The wire is insulated with enamel and I have to remove it before soldering it back onto the board.  How should I remove the enamel? Count how many lines start with which characters I have a file with a number of lines in a file filename.  I want to count how many lines start with character 'a', with 'b' and so on in one go.  What command i should execute.? Google Drive storage mismatch I have a paid 100GB Google Drive plan. It is reporting that I am at 99% capacity.  According to the the storage both within the desktop and web application, I have used 90.53GB within Drive.    My Drive is mapped to my OS X filesystem, and when fully synched it reports only 61.28GB used.    So what is going on here? I need to do a cleanup but cannot account for the 30GB difference. Max Planck, arguably the leading theoretical Physicist of his day, apparently used of experimental data to formulate his equation for , which was a major step in the birth of quantum mechanics. For this seminal event of the 20th century, I would expect a detailed explanation of how Planck arrived at his conclusion that energy MUST be quantized. I've even read his Nobel lecture but was non the wiser.  Can some kind person please explain it, or give me even just a hint? I am trying to install Microsoft Office 2013 on Ubuntu 12.04 LTS (32-bit). I have downloaded an iso file of said product and installed wine1.4-i386 using the apt-get command on the terminal.  The question is I don't know the steps how to install it. I can't get much tutorials on Internet how MSOffice2013 can be installed on Ubuntu.  If any versions of wine isn't an option, what other options can be used to run Microsoft Office 2013? How can I sum two values and store the result in other variable? Why is defragmentation unnecessary?