Separable differential equations 2

[taylornhunsucker]

I don't have to go to lecture ever again. Thank you so much.

[betonmolenislol]

you rock.

[WetHotFarts]

Test tomorrow, you just saved me

[zodei]

hey! How you solve this tan x dy/dx + y = sec x? =D

[Exploratorius12]

@zodei difficult question... divide by tan(x) to obtain the standard form of this 1st order linear ODE: y'+p(x)*y=q(x); p(x)=cot(x), q(x)=csc(x). multiply both sides by an integrating factor u(x) to obtain u(x)*y'+p(x)*u(x)*y=q(x). why? if u(x) is chosen carefully the product rule will simplify this to [1.1] (u(x)*y)'=q(x). for that to work u'(x) has to be p(x)*u(x), so u'(x)/u(x)=p(x), so ln(u(x))=p(x), so u(x)=e^integral(p(x)). use this to calculate u(x). plug it into [1.1]. integrate [1.1].

[Exploratorius12]

@zodei 'so ln(u(x))=p(x)', sry that was supposed to be 'ln(u(x))=integral(p(x))'... i was supposed to integrate both sides... the integral of u'(x)/u(x) is ln(u(x)) (due to the chain rule - just derive ln(u(x)) to check this) and i forgot to integrate the right hand side. in the next step i didn't make that mistake because i got u(x)=e^integral(p(x)). i realize these remarks can only be a hint to the actual solution but i still hope they are gonna be helpful.

[platazar]

PLEASE WHAT'S THE NAME OF THIS SOFTWARE ?

[dolnodjob]

@platazar MS Paint?

[UKGrahamUK]

y go to class for 50 mins when i can learn it in 5 mins, in my pj's

[PelicanGodOfJupiter]

With the four simple words "implicit differentiation in reverse" I suddenly had a door of understanding flung wide open by my new hero, you.

[TheDjchugz]

awesome...

[Laimmemo]

:))))))) SO HELPFUL

[Laimmemo]

:)))))))

[XeadXhot]

i'm unable to fine a video on non-homegenous differential equations, if you don't have one i guess this is just a suggestion.

Keep up the grerat work

[somethingonmyhip]

@XeadXhot

Just find a homegenous one (Yh) and a particular solution (Yp) Then Y = Yh + Yp

[MimiD3]

Like im sooo happy i could cry !!!! I finnally get this stuff... 

[xman9344]

thx (:

[p3s5h]

this video is so beautiful.

never in my entire life would i have said anything having to do with calculus is beautiful, but i needed serious help, and this video answered my cries. thank you so much, khan academy.

[drrojas]

At Khan Academy , the bell never rings! I wanna separably differentiate all day now

"In Khan We Trust".

[ynut666]

be my prof pls

[gdeep783]

3 dislikes? really? If Sal can't make you understand this, nobody can!!!

[wolterh6]

If one integrates with the x side without dividing by y in both sides of the equation, can the equation be solved anyway? It didn't work for me and I guess it cannot be solved, why?

[337punter]

You are so helpful. This makes math make sense. Thanks!

[hanz12891]

i don't know what more surprising...you explaining a semester worth's course in one sitting, or why im blowing $200,000 on professors who are good at nothing more than putting me to sleep

[TheJavaExpert]

i had knew anything before watching this then i just got a BB from diff. eqns.. u are a hero!

[Rizmaestro]

Thanks! Came home from school conpletely lost but you saved me!

[ooweirdoo]

my webwork asks for y= blah blah but i cant set them to one side :(

[Dimbnd]

"We have to separate the wives from the exes" I heard this and lol'd.

[321boileranimal]

I don't know nothing about no computers mister.

[321boileranimal]

I don't know nothing about no computers mister.

[jakub9983]

how can i solve this Sal? 6xy+e^y+(3x^2+xe^y)y'=0 Please give me advise on this. I'm totally lost.

[dalcde]

@jakub9983 It's not separable (actually most DEs aren't separable). Look at the videos on exact equations. I think it is exact.

[jakub9983]

@dalcde You are right, its exact. Thank you very much. Its so easy to solve when you know algorithm. :)

[alan48085]

y are u such a good teacher

[dalcde]

Is it possible to solve Maxwell's Equations?

[Forman6]

and now i can be a badass before i start differential equation.

[ches111]

we were dividing both sides by y, what about a case when y = 0?

[latenightsesh55]

STOP!

[disornr]

I really need to say "THANKS ALOT MAN!!!" you save my whole entire life!!

[louwas93]

is it possible to call these 'implicit integrals'?

[iloveuanonlyu]

@louwas93 i was wonderin the same tin

[shaunmikex]

Are professors bothered by you being 10x more concise than they are?

[doubleja]

@shaunmikex

theyJeLLy?

[ahage16]

@shaunmikex Sadly, I don't think most professors give a crap how well they teach.

[rabia22p]

I don't understand the second step where he takes the derivative =(

[zzackkkk]

@rabia22p Both sides were divided by y.

[TuscaniManiac]

Thanks ! 5*

[rizwanspirit]

Most useful videos i have ever seen on youtube

Thank you Khan bhai.

[mchk2]

I swear I am suing my school to get my money back for my EA class to give it to you lol, thanks!

[bkisme]

My friend and I had our calc teacher keep your website URL on the whiteboard for people to utilize. :)

[PrinceFX]

100th person to rate this vid a perfect 5/5 :D

[nemothecute]

You are a admirable mystery!

[SweetMusic223]

You would be a GREAT math professor, if you haven't been one. :D

[philg24]

You help me soo much!! THX VERY MUCH! YOU ARE A GREAT TEACHER!

[mvtrumpetgeek13]

Teacher of the year :)

[fettosh]

grate exeplination, this is the first time I understande math and have really intresst in math and want to learn more, thanks allote, you have change the world a grate deal.

just imagine if all school teachers could teach like you do!!!!

[wayofwei]

thank you so much for this (:

You cleared up A LOT of confusions that I have about this subject (my teacher who normally doesn't even teach that well was absent today so I was left to my own devices), and now I can do my homework (:

[b23571113]

how do you know what sinx is?

[katievstheworld]

google the "unit circle"

[BarbaraVValters]

@b23571113 Everyone how is tdowning you are homeless-the-sexuals.

When he substituted-in the initial value of "when x=0, y=1", sin(x) becomes sin(0). The triangle formed when the angle is zero has no vertical, or "opposite" component. Remember SOHCAHTOA? So, sin(0)=0.

You've probably figured that out by now, but if you had asked, then there are probably other people who've wondered the same thing.

[vivi17P]

thanks!!!!!

[bakopala]

Damn you are good i never got this shit in class

[hatemakingnamesup]

Great Explain : )

[TheWarTorn]

can anyone confirm that if you make y the subject you get y=e^[(sinx)/3]

[Tank878]

Dude! I wish you were our lecturer at uni - very helpful indeed.

[eur04lif3]

you should teach @ Clark!!! i wish my instructor expained that well....much thanks

[netrusher22]

youre a baller. thanks for the vids

[timo86m]

Hi i am new to Diff=tions but how come when he divided by y to get rid of y from right hand side, he did not divide the dy/dx by y?

[cagedkiller360]

He did not need to, since there was something already multiplying the dy/dx. When you have that situation, you only need to divide the multiplying quantity.

[shadowC10ne]

I think it's because dy/dx is multiplied by (1+2y^2).

[curtisjb1983]

5*4=2*x

divide both sides by 2, when you do this you get rid of the 2 on the right side and you can either divide the 4 by 2 or the 5 by 2 (which would be silly because that would give you a fraction, but the answer would still work out correctly)

So...

5*(4/2)=x

5*2=x

x=10

on his example you have two terms multiplied together as well so he chose the "easiest" term to divide into.

[standaman109]

you are def the man. thanks so much.

[gonzodercoole]

Thx for the effort man :)

[cwhc333]

super!

[dieharddd25]

just when i thought i was screwed, TNX! really helpful.

[Studentatmacomb]

you save lives!!!!!

Thank You and keep it up!

[AWorldsCreator]

I looooove these videos...

thank you!!

[gambuzo]

Fantastic, thank you !!!

I keenly anticipate the numerical solutions, which you have mentioned, for both differential equations and integration.

Once again, thank you.

[dave597]

Thanks for uploading!

[SteadyHaze]

king sal