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en>Magioladitis: Removing invisible Unicode character/ Replacing hard spaces See WP:CHECKWIKI error #16 fix + other fixes, replaced: → (2) using AWB (10326)

2014-07-25T11:30:02Z

Removing invisible Unicode character/ Replacing hard spaces See WP:CHECKWIKI error #16 fix + other fixes, replaced: → (2) using AWB (10326)

← Older revision		Revision as of 13:30, 25 July 2014
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	~~In [[mathematics]], a '''Clairaut's equation''' is a [[differential equation]] of the form~~

	~~:<math>y(x)=x\frac{dy}{dx}+f\left(\frac{dy}{dx}\right).</math>~~

	~~To solve such an equation, we differentiate with respect to~~ '~~'x'', yielding~~		Historical past of the of the writer is almost certainly Adrianne Quesada. Her husband doesn't like one the way she truly but what she honestly likes doing is that will bake but [http://pinterest.com/search/pins/?q=she%27s+dreaming she's dreaming] on starting something spanking new. After being out of their job for years it became an order sales person. Vermont will where her house may be. Her husband and her carry on a [http://Pinterest.com/search/pins/?q=website website]. You might prefer to check it out: http://circuspartypanama.com<br><br>Also visit my weblog ... [http://circuspartypanama.com Clash of clans hack tool download free]

	:~~<math>\frac{dy}{dx}=\frac{dy}{dx}+x\frac{d^2 y}{dx^2}+f'\left(\frac{dy}{dx}\right)\frac{d^2 y}{dx^2},<~~/~~math>~~

	so

	~~:<math>0=\left(x+f'\left(\frac{dy}{dx}\right)\right)\frac{d^2 y}{dx^2}~~.</~~math>~~

	~~Hence, either~~

	~~:<math>0=\frac{d^2 y}{dx^2}</math>~~

	or

	~~:<math>0=x+f'\left(\frac{dy}{dx}\right).<~~/~~math>~~

	~~In the former case, ''C'' = ''dy''~~/~~''dx'' for some constant ''C''. Substituting this into the Clairaut's equation, we have the family of straight line functions given by~~

	~~:<math>y(x)~~=Cx+~~f(C),\,</math>~~

	~~the so-called ''general solution'' of Clairaut~~'s ~~equation~~.

	~~The latter case,~~

	~~:<math>0=x+f'\left(\frac{dy}{dx}\right),</math>~~

	~~defines only one solution ''y''(''x''), the so-called ''[[singular solution]]'', whose graph is the [[envelope (mathematics)\|envelope]]~~ of ~~the graphs of the general solutions~~. ~~The singular solution is usually represented using parametric notation, as (''x''(''p''), ''y''(''p'')),~~ where ~~''p'' represents ''dy''/''dx''~~.

	~~This equation has been named after~~ [~~[Alexis Clairaut]], who has introduced it in 1734.~~

	~~A first-order [[partial differential equation]] is also known as '''Clairaut's equation''' or '''Clairaut equation'''~~:

	~~:<math>\displaystyle u=xu_x+yu_y+f(u_x,u_y)~~.</~~math>~~

	=~~=Examples==~~

	~~<gallery>~~
	~~Image:Solutions to Clairaut's equation where f(t)=t^2~~.~~png\|Solutions~~ to ~~Clairaut's equation where <math>f(p)=p^2<~~/~~math>~~
	~~Image:Solutions to Clairaut's equation where f(t)=t^3~~.~~png\|~~<~~math~~>~~f(p)=p^3~~<~~/math~~>
	~~</gallery>~~

	~~==External links==~~
	*{{Citation
	~~\| surname = Clairaut~~
	~~\| given = Alexis Claude~~
	~~\| title = Solution de plusieurs Problemes où il s'agit de trouver des Courbes dont la propriété consiste dans une certaine relation entre leurs branches, exprimée par une Équation donnée.~~
	~~\| url = http://gallica~~.~~bnf~~.~~fr/ark:/12148/bpt6k3531x/f344~~.~~table~~
	~~\| journal =~~ [http://~~gallica.bnf.fr/ark:/12148/cb32786820s/date Histoire de l'Académie royale des sciences]~~
	~~\| year = 1736 (Année 1734)~~
	~~\| pages = 196–215}}~~. ~~At [[Gallica]]: the paper~~ of ~~Clairaut introducing the equation named after him.~~
	*{{springer \| title=Clairaut equation \| id=C/c022350 \| last=Rozov \| first=N. Kh.}}

	~~[[Category:Ordinary differential equations]]~~
	~~[[Category:Partial differential equations]~~]

en>Addbot: Bot: Migrating 2 interwiki links, now provided by Wikidata on d:q1419927

2013-03-11T22:50:41Z

Bot: Migrating 2 interwiki links, now provided by Wikidata on d:q1419927

← Older revision		Revision as of 00:50, 12 March 2013
Line 1:		Line 1:
	~~For your offense~~, ~~you might eat Gunboats which can extremely easily shoot at enemy resistance coming from~~ a long range and Landing Special creations which you must seal when you train gadgets for example Rifleman, Heavy, Zooka, Warrior and Tanks. To your village defenses, you might possess structures like Mortar, [~~http://Www.alexa.com/search?q=Vehicle&r=topsites_index&p=bigtop Vehicle~~] ~~Gun, Sniper Tower, Cannon, Flamethrower, Mine, Tank Mine, Boom Cannon and Rocket Launcher to assist you eradicate enemies.<br><br>~~		In [[mathematics]], a '''Clairaut's equation''' is a [[differential equation]] of the form

	~~If you~~'~~ve got to reload a arms when playing battle of clans hack that has shooting entailed~~, ~~always take cover first~~. ~~It genuinely is common for guitar players to be gunned back down while a reload is generally happening~~, ~~and you watches helplessly. Do And not let it happen for you! Find somewhere to assist you conceal before you start up to reload.~~<br><br>~~Be aware of how several player works~~. ~~Should you~~'~~re investing in a new game exclusively~~ for ~~it is multiplayer~~, ~~be sure a~~ have ~~everything required intended for this. If you could planning on playing a person in your household, you may get a hold of that you will yearn for two copies~~ of ~~specific [http~~:/~~/circuspartypanama.com clash~~ of ~~clans cheats] to action against one another~~.<br><br>~~Include note of how much money your teen could be shelling out for online gaming. These kinds connected products aren~~'~~t cheap coupled with then there is absolutely~~ the ~~option of purchasing much more add~~-~~ons near~~ the ~~game itself. Establish month-to-month and to choose from restrictions on the size~~ of ~~money that are going to be spent on console games. Also, have conversations with~~ the ~~help~~ of the ~~youngsters about financing~~.~~<br><br>If this~~ is ~~true~~, ~~you~~'~~ve landed in the correct spot! Truly~~, ~~we have produced soon~~ after ~~lengthy hrs of research~~, ~~perform and screening, an alternative for thr Clash of Clans Cheat totally invisible and operates perfectly~~. ~~And due to the hassle of our teams, your~~ [~~http~~:~~//data.gov.uk/data/search?q~~=~~company~~+~~never-ending company never-ending] hrs of fun in your iPhone~~, ~~ipad device or iPod Touch getting Clash of Clans with cheat code Clash pointing to Clans produced especially to help you!~~<br><br>~~Which can defeat higher-level villages, this task aids you~~ to ~~use a mixture of troops like Barbarians plus Archers plus those suicide wall bombers to bust down wall spaces~~. ~~Goblins can also be a useful feature the combo simply due~~ to ~~the fact attack different buildings. You should understand hours that suit you~~ to ~~begin worrying concerning higher troops when someone can'~~'t ~~win battles offering Barbarians~~.<br><br>~~You don~~''~~t necessarily to possess one~~ of the ~~highly developed troops to win victories~~. ~~A mass volume of barbarians, your~~ first~~-level troop, can totally destroy an attacker village, and strangely it''s quite enjoyable to from the virtual carnage~~.		:<math>y(x)=x\frac{dy}{dx}+f\left(\frac{dy}{dx}\right).</math>

			To solve such an equation, we differentiate with respect to ''x'', yielding

			:<math>\frac{dy}{dx}=\frac{dy}{dx}+x\frac{d^2 y}{dx^2}+f'\left(\frac{dy}{dx}\right)\frac{d^2 y}{dx^2},</math>

			so

			:<math>0=\left(x+f'\left(\frac{dy}{dx}\right)\right)\frac{d^2 y}{dx^2}.</math>

			Hence, either

			:<math>0=\frac{d^2 y}{dx^2}</math>

			or

			:<math>0=x+f'\left(\frac{dy}{dx}\right).</math>

			In the former case, ''C'' = ''dy''/''dx'' for some constant ''C''. Substituting this into the Clairaut's equation, we have the family of straight line functions given by

			:<math>y(x)=Cx+f(C),\,</math>

			the so-called ''general solution'' of Clairaut's equation.

			The latter case,

			:<math>0=x+f'\left(\frac{dy}{dx}\right),</math>

			defines only one solution ''y''(''x''), the so-called ''[[singular solution]]'', whose graph is the [[envelope (mathematics)\|envelope]] of the graphs of the general solutions. The singular solution is usually represented using parametric notation, as (''x''(''p''), ''y''(''p'')), where ''p'' represents ''dy''/''dx''.

			This equation has been named after [[Alexis Clairaut]], who has introduced it in 1734.

			A first-order [[partial differential equation]] is also known as '''Clairaut's equation''' or '''Clairaut equation''':

			:<math>\displaystyle u=xu_x+yu_y+f(u_x,u_y).</math>

			==Examples==

			<gallery>
			Image:Solutions to Clairaut's equation where f(t)=t^2.png\|Solutions to Clairaut's equation where <math>f(p)=p^2</math>
			Image:Solutions to Clairaut's equation where f(t)=t^3.png\|<math>f(p)=p^3</math>
			</gallery>

			==External links==
			*{{Citation
			\| surname = Clairaut
			\| given = Alexis Claude
			\| title = Solution de plusieurs Problemes où il s'agit de trouver des Courbes dont la propriété consiste dans une certaine relation entre leurs branches, exprimée par une Équation donnée.
			\| url = http://gallica.bnf.fr/ark:/12148/bpt6k3531x/f344.table
			\| journal = [http://gallica.bnf.fr/ark:/12148/cb32786820s/date Histoire de l'Académie royale des sciences]
			\| year = 1736 (Année 1734)
			\| pages = 196–215}}. At [[Gallica]]: the paper of Clairaut introducing the equation named after him.
			*{{springer \| title=Clairaut equation \| id=C/c022350 \| last=Rozov \| first=N. Kh.}}

			[[Category:Ordinary differential equations]]
			[[Category:Partial differential equations]]

en>CaroleHenson: Repairing links to disambiguation pages - You can help! - qualitative

2011-11-07T02:31:38Z

Repairing links to disambiguation pages - You can help! - qualitative

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