solve the following equation : $$yy''=y^2y'+(y')^2$$ I have tried this question by using a special case of the second-order differential equation, but I stuck when it comes to three unknown
I am asked to solve this ODE: $$yy''-y'y^2-(y')^2=0.$$ Can I get some guidelines on how I can solve it? I am not sure how to approach without initial conditions.
What's the typical microclimate in the aircraft passenger cabin? I know some countries such as UK has the steering wheels of their cars on the right side. But as we can see, most of the Europian countries uses it at the opposite side. Since I used to drive a car with left-steering wheel I found it impossible to drive a car with right-steer!  Not curiosity, but I am trying to map if this issue is related to User Experience or not. 1) Up until now, during practical work sessions, I always used these formulas for uncertainty propagation:  if $C = A+B$  or  $C = A-B$ $$\Delta C = \Delta A + \Delta B$$ if $C = AB$ or $C = \frac{A}{B}$ $$\frac{\Delta C}{C} = \frac{\Delta A}{A}  + \frac{\Delta B}{B}$$ if $C = A^m$ $$\frac{\Delta C}{C} = |m|\frac{\Delta A}{A}$$   These formulas are derived from the expression for the differential of a function of multiple variables:  if $C = f(A,B)$ $$ dC = \frac{\partial C}{\partial A}dA + \frac{\partial C}{\partial B}dB \Rightarrow \Delta C = \frac{\partial C}{\partial A}\Delta A + \frac{\partial C}{\partial B}\Delta B$$  and I think that makes sense because the value C is just a function of two variables that happen to be measurements.  2) But this morning, I was told that this is wrong and I should actually use these instead:  if $C = A+B$  or  $C = A-B$ $$(\Delta C)^2 = (\Delta A)^2 + (\Delta B)^2$$ if $C = AB$ or $C = \frac{A}{B}$ $$\left(\frac{\Delta C}{C}\right)^2 = \left(\frac{\Delta A}{A}\right)^2  + \left(\frac{\Delta B}{B}\right)^2$$  which are apparently derived from a general formula:  $$(\Delta C)^2  = \left(\frac{\partial C}{\partial x_1}\Delta x_1\right)^2 + \left(\frac{\partial C}{\partial x_2}\Delta x_2\right)^2 +   \hspace{0.3cm}...$$  or   $$\Delta C  = \sqrt{\left(\frac{\partial C}{\partial x_1}\Delta x_1\right)^2 + \left(\frac{\partial C}{\partial x_2}\Delta x_2\right)^2 +   \hspace{0.3cm}...}$$  3) So:   Why is this formula better?  Where does it come from? What does it actually represent? (Do I recognize the shape of a norm in that last formula?)  What is wrong with the formula of the differential?   I'm asking a lot, but the propagation of uncertainty always confused the ship out of me. When should the "Not an Answer" flag be used? Proof of Dobinski's formula for Bell numbers How can I publish my game (*.aab file) on google play? Where can I find good ConTeXt documentation Avoiding if statement inside a for loop? When do moderator elections take place? I'm really confused on this. I have no idea on several things:   When do elections begin?   Is there a set time each year?   Do elections actually take place each year?   Can I vote?   Where do I vote?     Etc.  Can someone please help me? Interpreting Granger causality test's results I'm trying to educate myself on Granger Causality. I've read the posts on this site and several good articles online.  I also came across a very helpful tool, the , that allows you to enter your time series and calculate the Granger Stats.  Below, is the output from the sample data included on the site. I have also taken a crack at interpreting the results.   My Questions:     Is my interpretation directionally correct?   What key insights have I overlooked?   Also what is the meaning and interpretation of the CCF charts?  (I'm assuming CCF is cross correlation.)     Here are the results and plots that I have interpreted:  Summary of computational transaction Raw Input   view raw input (R code) Raw Output  view raw output of R engine Computing time  2 seconds R Server    'Herman Ole Andreas Wold' @ wold.wessa.net  Granger Causality Test: Y = f(X) Model   Res.DF  Diff. DF    F   p-value Complete model  356          Reduced model   357 -1  17.9144959720894    2.94360540545316e-05  Granger Causality Test: X = f(Y) Model   Res.DF  Diff. DF    F   p-value Complete model  356          Reduced model   357 -1  0.0929541667364279  0.760632773377753       My interpretation:    Test was based upon 357 data points and was performed with a lag value of 1 The p-value of 0.0000294 means I can reject the null hypothesis that x does not cause y for the Y = f(x). The p-value of .76 allows me to accept the null for X = f(Y) The fact that first hypothesis was rejected and second accepted is a good thing  I'm a little rusty on my F-test so I don't really have anything to say on this for now. I'm also not sure how to interpret the CCF graph.   I really appreciate it if any of you who are well versed with Granger-causality could let me know if I'm interpeting this correctly and also fill in some of the blanks.   Thanks for your help. Approximating a $\sigma$-algebra by a generating algebra Theorem. Let $(X,\mathcal B,\mu)$ a finite measure space, where $\mu$ is a positive measure. Let $\mathcal A\subset \mathcal B$ an algebra generating $\cal B$. Then for all $B\in\cal B$ and $\varepsilon&gt;0$, we can find $A\in\cal A$ such that $$\mu(A\Delta B)=\mu(A\cup B)-\mu(A\cap B)&lt;\varepsilon.$$  I don't think there is a proof in this site. It's a useful result for several reasons:  We know what the algebra generated by a collection of sets is, but not what the generated $\sigma$-algebra is. The map $\rho\colon \cal B\times\cal B\to \Bbb R_+$, $\rho(A,A')=\mu(A\Delta A')$ gives a pseudo-metric on $\cal B$. This makes a link between generating for an algebra and dense for the pseudo-metric. We say that a $\sigma$-algebra is separable if it's generated by a countable class of sets. In this case, the algebra generated by this class is countable. An with the mentioned result, we can show that $L^p(\mu)$ is separable for $1\leq p&lt;\infty$, which makes a link between the two notions. In ergodic theory, we have to test mixing conditions only an a generating algebra, not on all the $\sigma$-algebra. We need a hard rate limit on suggested edits, to limit the damage someone can do with blasting the review queue with minor edit suggestions.  Case in point:  peppered the site with a whopping 133 tag-only edit suggestions in 2 hours and 15 minutes. That's one edit every minute on average, but towards the end he was entering a new suggestion every 20 seconds. He only stopped because a  drew enough rejections to have him banned from entering more.  If there was a limit to the number of suggested edits you can enter in a time period we could have stopped this guy earlier. No &lt;2k user needs to edit hundreds of tags across that many questions in 2 hours time.  Considerations   There are cases where a retag drive or tag burninate justifies editing a larger number of posts, but I'd be fine if such tasks were limited to people with 2k+ reputation. A retag or burninate job requires a minimal engagement with the community to know when they are justified anyway. The suggested edit review process, by itself, was clearly not enough to stop this barrage. It cannot be seen as a rate limiting measure, at least not as a sufficiently efficient one.  The vast majority of the edits made in the above example were too minor, leaving spelling, grammar and formatting mistakes in the post untouched. The user was going too fast to pay attention to such details anyway. Yet this user has 98 approved edit suggestions, but all but 6 or 7 I'd have rejected as too minor, so the review process itself is broken.   What should be limited   The number of review votes reviewers have is already limited; I burned through 20 reviews in short order just reviewing the suggestions from just this one user. Certainly the number of unreviewed suggestions should be limited to let reviewers catch up with a user like this. I'd say having 20 outstanding suggested edits pending review is plenty. Suggested edits should be made with some consideration; we don't want minor edits, so if you are suggesting more than 20 in an hour (that's 1 every 3 minutes) you are not improving posts anymore, you are gaming the system to gain reputation. crisscross, dillydally, riffraff, etc Posting to friends' wall with Graph API via 'feed' connection failing since Feb 6th 2013 Notification email from stackoverflow contains "<3" after zip code Google Chrome won't install on 17.04 I had to remove Chrome to have enough space to upgrade from 16.10 to 17.04.  I downloaded the latest version from Google.  But when it opens in the Ubuntu Software Manager, and I click on "Install", nothing happens. How can I check which songs or videos that I purchased from the iTunes Store have DRM restrictions?  All of the mobile OSes are very impressive to me at the moment, and I'm thinking about trying a non-iOS device again. I want to know now the impact it has on my Apple-sourced music collection though.  Is there a date cut-off for purchases when items went DRM free? Extrusions causing problems in edit mode When I extruded vertices in edit mode, for some reason one of the sides of my 3-D model (the textured-looking side to the right) is creating a lot of errors. First off, it automatically sets extrusions on the x-axis. Secondly, it doesn't allow me to extrude planes into 3-D shapes. Thirdly, I can't increase the height of vertices without it creating a new face. Finally, it renders those automatic textures to create a grainy black texture in render mode. I attached an image with the solid object (top) and the rendered object (bottom). Note: I did not set any textures or alter the lighting on the model. Also, the left gray side is working perfectly fine without errors. For the following block of code:  For I = 0 To listOfStrings.Count - 1     If myString.Contains(lstOfStrings.Item(I)) Then         Return True     End If Next Return False   The output is:  Case 1:  myString: C:\Files\myfile.doc listOfString: C:\Files\, C:\Files2\ Result: True   Case 2:  myString: C:\Files3\myfile.doc listOfString: C:\Files\, C:\Files2\ Result: False   The list (listOfStrings) may contain several items (minimum 20) and it has to be checked against a thousands of strings (like myString).  Is there a better (more efficient) way to write this code? A linking verb is a verb which connects a subject to its predicate   without expressing an action. A linking verb is used to re-identify or   describe its subject.      Ex:      Alan is a beast.      Alan seems drunk.   But I would say that some linking verbs can be used with "continuous tenses" &amp; other linking verbs can not, but I am not sure.      (linking verb) to experience a particular feeling or emotion      Ex: I’m feeling a little better today.      Do you still feel hungry?   So, feel in this meaning can be used with continuous tenses  But I would think this sentence "Do you still feel hungry?" does not make much sense because it uses "simple present tense" which expresses something that happens regularly. Noone would feel hungry regularly.  So, that sentence "you feel hungry" would mean "you always feel hungry".      (linking verb) (not used in the progressive tenses): to have a   particular physical quality which you become aware of by touching         adj.         The water feels warm.      Its skin feels really smooth.    says "Speakers sometimes use the Simple Present to express the idea that an action is happening or is not happening now. This can only be done with Non-Continuous Verbs and certain Mixed Verbs."  so, "The water feels warm." could mean "The water is always warm" (simple present expressing things that happen regularly - more or less permanent action)  But "The water feels warm." could mean "The water is warm now" (simple present with non-continuous verb expressing things that is happening now - a temporary action)     : (linking verb) to seem; to appear         adj.         to look pale/happy/tired      That book looks interesting.   In dictionary,      (linking verb) (not used in the progressive tenses): to   give the impression of being or doing something         adj.         She didn't appear surprised at all.       (to somebody) (to be) something (not used in the progressive tenses): to give the impression of being or doing something (synonym:   appear)         adj.         You seem happy.   So, we cannot say "you are seeming happy" or "you are appearing happy".  But I am not sure I can say "You are looking good" (sounds right to my ears) or "That book is looking interesting." (doesn't sound right to my ears)  But we can say "The future’s looking good." ()  So, some verbs has the same meaning but one can be used with "continuous" &amp; the other can not, right?  Ex: "you are looking happy", but "you seem happy".