I apologise, since this question does already exist. But I cannot for the life of me understand how it is solved. Could anyone provide me with a simplified version of the solution?
I am asked to solve $$u_x+u_y=1$$ If is was homogeneous i.e., $u_x+u_y$ the answer would be $u(x,y)=f(y-x)$ where $f$ is an arbitrary function. I have found the following set of solutions: $$u(x,y)=\lambda x +(1-\lambda)y$$ where $\lambda$ is an arbitrary constant(real or imaginary). I just have no idea what method other then trial and error would have lead me here. Any ideas? Thanks!
Ubuntu does not offers me "install alongside Windows" Any of the partitions makes in Windows was not recognised by Ubuntu, or Zorin OS, or LinuxMint. It's like a blank hard disc, 250 gb free. I'm a new Linux user, but what confuses me is that I was able to install Ubuntu alongside Windows on my laptop with no problems, but on PC... no way! Does "no larger than" imply shapability? I am always confused about where to put adverbs in sentences. For example, consider the questions below:        Why did they target us specifically?   Why did they target specifically us?   Why did they specifically target us?      I believe all these sentences mean the same. Am I correct? I am always confused about where to put adverbs such as always and specifically, etc. Is there a particular grammar rule for this?  Funny, you see, I can even form the above sentence in different ways.         I always confuse where to put this kind of adverb   Always I confuse where to put this kind of adverb "You should be well-organised" or "You should be well organised"? How to enable multiple logon remote desktop in Windows 7 Is Autopilot Openstack 16.04 available? Consider the function : $$f: \mathbb{R}^2 \rightarrow \mathbb{R} , (x,y) \mapsto   \begin{cases}         0 &amp; \text{for } (x,y)=(0,0) \\    \frac{x^3}{x^2+y^2}       &amp; \text{for } (x,y) \neq (0,0)   \end{cases} $$  Show that $f$ not differentiable at $(0,0)$ but all directional derivatives exist.  I don't know how to tackle this problem. Can someone give some hints or solve the problem? Thanks :) \includegraphics: Dots in filename \includegraphics cannot handle filenames that contain more than the one dot, separating the filename from the extension. Apparently it uses everything after the first dot as extension and then, of course, complains about an unknown graphics extension.  This is annoying as I very often have filenames that contain parameter values, e.g. plot_a0.4_b0.6.pdf.  Is there a way to teach LaTeX to interpret only the string behind the last dot as extension? Short story or novel from the 1970s or before about two warring alien tribes Could the universe's antimatter be hiding in black holes? As far as we know almost all the mass in the universe is matter, not antimatter. There are three scenarios:   The universe started off with more matter than antimatter and the small amount of antimatter has mostly been converted to energy via collisions with matter The universe started off with equal amounts of matter and antimatter and some unknown process caused the situation we see today The universe started off with less matter than antimatter and somehow the ratio reversed (I've never heard this discussed as it seems so unlikely)   We reason that mass is matter because if there were large amounts of antimatter they should produce antimatter galaxies, which would give off huge amounts of energy when they interact with matter galaxies. This has never been observed so we conclude that all galaxies, therefore all mass in the universe is matter.  As I understand it there are two main types of black holes, stellar remnants (the collapsed remnants of dead stars with more than two solar masses) and super-massive black holes at the centre of many galaxies, including one thought to be at the centre of our own galaxy.  Stellar black holes are obviously originally composed of matter, for the same reason that all galaxies are composed of matter.  We don't know how super-massive black holes formed. Is there enough mass in them to contain all the antimatter in the universe if matter and antimatter were originally created in equal quantities? I realise this shifts the unknown mechanism from "why was more matter created than antimatter" to "why is antimatter more likely to form super-massive black holes" but is this hypothetical scenario possible? Word for "reading carefully" Sometimes we read books rather quickly and don't give them much (or any) thought, so the action 'reading' does not necessarily imply that we have given enough thoughts to any book we read.   Is there a word that describes reading a book with great care; usually but necessarily slowly over a long period of time. Mount cifs Network Drive: write permissions and chown I have access to a cifs network drive. When I mount it under my OSX machine, I can read and write from and to it.   When I mount the drive in ubuntu, using:  sudo mount -t cifs -o username=${USER},password=${PASSWORD} //server-address/folder /mount/path/on/ubuntu   I am not able to write to the network drive, but I can read from it. I have checked the permissions and owner of the mount folder, they look like:  4.0K drwxr-xr-x  4 root root    0 Nov 12  2010 Mounted_folder   I cannot change the owner, because I get the error:  chown: changing ownership of `/Volumes/Mounted_folder': Not a directory   When I descend deeper into the network drive, and change the ownership there, I get the error that I have no permission to change the folder´s owner.  What should I do to activate my write permission? What would you see if you have 2 huge mirrors (you cant look over it or next to it)  You place them with the reflecting side to each other and you look in the mirror from behind one mirror (one way mirror = 1 side glass 1 side mirror, like in a movie when cops are questioning a suspect.)  The mirror would reflect each other endless.  The example could be preformed with a see trough mirror (1 side mirror other side glass) but I don't have one, also I don't have huge mirrors.    Would it make a diffrence if you place a light source and if you dont have a light source?  My guess is that you would always see black because there is nothing to mirror.  Edit important:   There is nothing in the room to reflect on, so it only reflects the mirror, thats what i ment. How to remove selected commit log entries from a Git repository while keeping their changes? I would like to remove selected commit log entries from a linear commit tree, so that the entries do not show in the commit log.  My commit tree looks something like:  R--A--B--C--D--E--HEAD   I would like to remove the B and C entries so that they do not show in the commit log, but changes from A to D should be preserved. Maybe by introducing a single commit, so that B and C become BC and the tree looks like.  R--A--BC--D--E--HEAD   Or, ideally, after A comes D directly. D' representing changes from A to B, B to C and C to D.  R--A--D'--E--HEAD   Is this possible? if yes, how?  This is a fairly new project so has no branches as of now, hence no merges as well. Is there any way to check whether a file is locked without using a try/catch block?    Right now, the only way I know of is to just open the file and catch any System.IO.IOException. Why isn't apt full-upgrade getting an updated software key signature for skype After a recent apt update &amp;&amp; apt full-upgrade I started getting the following error when running apt full-upgrade subsequently: Get:4 https://repo.skype.com/deb stable InRelease [4,502 B]                                         Err:4 https://repo.skype.com/deb stable InRelease   The following signatures were invalid: EXPKEYSIG 1F3045A5DF7587C3 Skype Linux Client Repository &lt;se-um@microsoft.com&gt; W: An error occurred during the signature verification. The repository is not updated and the previous index files will be used. GPG error: https://repo.skype.com/deb stable InRelease: The following signatures were invalid: EXPKEYSIG 1F3045A5DF7587C3 Skype Linux Client Repository &lt;se-um@microsoft.com&gt; W: Failed to fetch https://repo.skype.com/deb/dists/stable/InRelease  The following signatures were invalid: EXPKEYSIG 1F3045A5DF7587C3 Skype Linux Client Repository &lt;se-um@microsoft.com&gt; W: Some index files failed to download. They have been ignored, or old ones used instead.  Is there a way to correct this, or is it down to Microsoft/Canonical to produce/update the necessary key signatures? CS0120: An object reference is required for the nonstatic field, method, or property 'foo' Can Quantum Entanglement and Quantum Superposition be considered the same phenomenon? Quantum entanglement is known to be the exchange of quantum information between two particles at a distance, while quantum superposition is known to be the uncertainty of a particle (or particles) being in several states at once (which could also involve the exchange of quantum information for a particle that is known to be in several locations simultaneously).  I was wondering if all of this was nothing more but the exchange of quantum information between different masses, and if this could clear up all the confusion in terms of how quantum systems connect in this field of science.  A clear explanation for how both of these quantum phenomena work, and if they really are connected (the exchange of quantum information?) would be much appreciated. Where To start Learning With Salesforce Development Grub not showing on startup for Windows 8.1 Ubuntu 13.10 Dual boot