We are asked to show that $$\left|\dfrac{\mathrm dy}{\mathrm dx}\right|+\left|y\right| +1=0$$ has no real solutions.    My proposed solution: Of course, $\left|\dfrac{\mathrm dy}{\mathrm dx}\right|$ and $\left|y\right|$ are non-negatives and 1 is positive. So, sum of all three of them can't be equal to zero (must be positive here) for any function $y=f(x)$.    My question: Is this argument strong enough to show that the ODE has no real solutions?
The given differential equation $$\lvert{dy\over{dx}}\rvert\,+\mid{y}\mid+1=0 $$  I don't know how to deal with modulus sign in order to prove the statement  Reference-Different Equations by Shipley L Ross Ch1 Exercise 7(a)
Using "that" and "this" interchangeably What is a magic number, and why is it bad? What is a magic number?  Why should it be avoided?  Are there cases where it's appropriate? Last night I was updating my Ubuntu 10.04 to either 11.04 or 12.04 (I'm not entirely sure which one it was, but I think it was 11.04) and I left it overnight to finish. When I came down in the morning, I noticed that the computer hadn't barely begun installing the updates! The update thing said that my computer was on the installation step, but it was still preparing the libc bin (or whatever its called) . It's like the first part of the step installing the upgrades. So, I stupidly restarted the computer, and when it rebooted, I got five options on a purple screen:  Ubuntu, with Linux 3.0.0-28-generic Ubuntu, with Linux 3.0.0-28-generic (recovery mode) Previous Linux versions Memory test (memtest86+) Memory test (memtest86+, serial console 115200)   Long story short, not matter which way I enter Ubuntu to try and reinstall the updates using the root thing (it's like terminal) after I enter sudo apt-get update it basically said it failed to fetch every url link, and it then says:  W: Some index files have failed to download. They have been ignored, or old ones used instead. W: Not using locking for read only lock file /var/lib/dpkg/lock E: dpkg was interrupted, you must manually run 'sudo dpkg --configure -a' to correct the problem.   So, I entered sudo dpkg --configure -a, and it says:  dpkg: error: unable to access dpkg status area: Read-only file system"   I'm left like wtf, and I really just some guidance here. I just got this laptop, and I can not afford a new one if I broke this one. Why is physical space equivalent to $\mathbb{R}^3$? I have a text file named "Hex_data.txt". I want to load content of Hex_data.txt into a variable name RAM in verilog. When I try this, I get an error that the text file can't be found. Where is this file loaded from?  The content of "hex_data.txt" :            21            a4          2a          26          7a          ff           6f   I want to create a variable name "RAM" defined like:   reg [6:0] RAM; in which the above content save like:  RAM[0]=21     RAM[1]=a4           RAM[2]=2a             RAM[3]=26            RAM[4]=7a             RAM[5]=ff             RAM[6]=6f   I wrote a code:  module file_read;      reg [7:0] RAM [0:6];          initial $readmemh("Hex_data.txt", RAM);   integer i;               initial begin                    $display("data:");                for (i=0; i &lt; 7; i=i+1)                $display("%d:%h",i,RAM[i]);              end                 endmodule        But the above code not working. How can i get desired output? I am trying to create buffers around the Hurricane Sandy path I created in QGIS (points are lat/long).   I have both points from each day she was tracted and the line I created from it with Points2One.   When I go to make buffers around either the line or the points, the buffer takes up the whole screen. Its all just one color.   I have made buffers before but from data I did not create.   Right now all of my projections are set to WGS 84 EPSG 4326. How To Reduce Noise In Cycles Render So this is my first try with cycles and I was wondering what can I do to make the image clearer? Can it hurt to put my GRE score on my resume? If my score is good and if I'm applying for an MS program in Europe, can it give me any kind of edge? The university I'm applying to requires GRE scores for certain programs but not the one I'm applying for. And if it won't be advantageous, can it hurt my prospects in anyway? Cancellation of Direct Products Can someone explain how Kat experienced this part of Tenet from her perspective? Recently, I read this  about how they have some of their infrastructure laid out. I was curious to know, does Stack Exchange use caching (both at the application layer and/or database layer) and if so, how? I have two lightning component placed on one page lightning app. First Component have refresh icon and I set onclick action to refresh Component $A.get('e.force:refreshView').fire(); but this event refresh the whole page instead of First component.  how can refresh only one component on page not all the page ? How to salt PBKDF2, when generating both an AES key and a HMAC key for Encrypt then MAC? When using Encrypt-then-MAC with AES and HMAC by password, and given 128 bits of payload with the ciphertext to store a random salt, which would be more secure:   Using PBKDF2 with then entire 128 bit random salt and generating 512 bits of derived data to split into a 256 bit AES Key and a 256 bit HMAC key.   or   Using PBKDF2 separately for each key using two 64 bits salts to generate a 256 bit AES Key and a 256 bit HMAC key.    or    Better option? How do I go about proving this?  If $\gcd(a,b)=1$ and $\gcd(a,c)=1$, then $\gcd(a,bc)=1$. I'm very confused with gcd proofs. How can I determine which process owns a hotkey in Windows? Given a hotkey, how can I find which program owns it? Prove that $Ax=0$ has infinite solutions if and only if $ \text{rank}(A)&lt;n$   Here is one way of my if proof, but I don't know how to proof the other part.  Let $r$ be the rank of $A$. Then $ r\leq  n$. If $ r&lt;n$, then there are $n-r$ linearly independent solutions. Furthermore any linear combination of these solutions will also be a solution of $Ax=0$. Hence, in this case, the equation $Ax=0$ has infinite number of solutions Training involved to ride 175 miles (281 km) in a day I want to be able to ride 175 miles (281 km) in a day (to do the ). I used to be able to do about 60 miles (96.5 km), only once hitting 80 miles (128 km), but I'm out of shape now. Wondering how I can systematically train to get to 175 miles at an average of 15 mph (24 km/h) Are there guides out there to help with this?  What's some advice?  [update] The  will happen each year, so my intention isn't to ride this year, rather what do I need to do to ride it in some future year? What is the difference between '->' (arrow operator) and '.' (dot operator) in Objective-C? How do I change the icon for a particular file type? I'm trying to change the icon for application/x-hwp files. I've added the icons to the proper places, and checked it with assoGiate (after reading ). It shows that my desired icon is associated with the file type. Nevertheless, Nautilus is still showing the old icon. How can I make Nautilus show the correct icon? How to make tr aware of non-ascii(unicode) characters?