Separable Differential Equations

[TRlPZ]

can't you just cross multiply when separating dx and dy?

[Dr3amerPT]

Am I the only who who smiled as soon as the word integrals was said? :D

[27shua27]

I have a question regarding whether or not an equation is linear.. You said even if in your first example it was a y instead of a squared it would be non linear because it is the same as having the derivative multiplied by Y, but if the situation were the same except you were multiplying by Y on the right and the derivative were on the left would it still be non linear because you could just divide both sides by Y and the derivative would be divided by Y or times Y to the negative first?

[anakmudajaman]

I Love The Video Introduction to separable differential equations. It Can Increase My Knowledge

[AntoMelta]

Good, I like that you share this video Introduction to separable differential equations, I wish success always

[willamricard]

Nice Video Introduction to separable differential equations That You Share , So Very Nice Thanks You

[imegatrone]

I Really Like The Video Introduction to separable differential equations From Your

[bundawartini]

Your Video Introduction to separable differential equations Is Very Useful Sharing

[Aelfredus26]

I love how he gets so excited near the end of the video :P

[loismen15]

Can we really just pass the dx to the left side of the equation? in my calculus class we can't do it...we have to solve the equation in a diferent way

[middleCmusic]

Great explanation as always, Sal!!

[MrTanookiMario]

It seems to me that your last few steps are unnecessarily limiting the relationship between x and y. Sure it says y(0)=-1, but it doesn't say that y(0) doesn't *also* equal 3.

But I think I'll forgive you, haha.

[pamBBB]

u have a very nice sounding voice. lol. thx for the math help!

[RookFx]

Easy to listen to, easy to follow. Great work!

[brunic11]

got my midterm in four hours.. thanks man great job totally put the finishing touches on how to do all of these :) life saver... if i pass i will subscribe

[datCRUNKbuay]

Why can't i grasp this? Any ideas./natural ways to improve concentration ?

[episkeys]

Thank you! I've been struggling with this for quite a while (partly because i've been feeling extremely tired in lectures and therefore, can't seem to catch up), so having this tutorial REALLY HELPED. I'm having my exam in about 2 weeks so yep. IM ON THE ROLL HEREEEE :D

[nosenseofconseqence]

KHHHAAAAAAAAAAANNNNNN!

you're awesome. thank you for influencing me in majoring in mathematics. you got me through my first year calculus courses, and I can see you helping me through most of the remainder of my degree :). This is gonna be a sick ride, thanks so much

[067077]

this makes so much more sense than my differential equations textbook, thanks!

[victorfergn]

differentials aren't numbers :P you can't solve it in that way

[newbobo]

yes the power of integrated in magenta

[Acerola211]

You should really use parentheses, Sal ^^;

[niconikko]

Question:

I noticed:

1(+-)2:

1+2 = 3 which is the constant

1-2 = -1 which is the initial condition

Are these two equations related?

[boxsaspen]

can't this be another solution for y, y=x^3+2x^2+2x-1 ???

[HunteronX]

Thank you very much for these videos. They are very helpful!

[MimiD3]

I GET IT !!! omg i have no idea what my proffesor has been saying !!! now i do !!! I truelly deeply appreciate this !! YOU ROCK !!

[natzo89]

I think learned more in half an hour here than in 3 months in my class.

[SAPHIRALEGEND545]

You are amazing :D THANKSS!

[ranile1]

wow! your the best! thank you!

[dytryn09]

you are a math god

[ejdugayo]

nice one!

[criznell]

While I made a B in Diff' EQ (...Baller), that was some time ago. I am preparing for the Fundamentals Exam and am very grateful for your videos. Thank You.

[tketai82]

if i need something simplified i always come to you! Thank you thank you saved my evening :-)

[irfuzizmar]

great job, keep up the work!

[Texanul1]

Man the differential eq it's hard shit and fuck my teacher mother fucker piece of shit

[joshnaire]

c=3 LOL .. looks like 8=D facing left

[skyewalker123]

So I am in my 4th week in my DiffEq class, completely lost, found these, and now I know everything. I may be in love with you .

[stsegay1]

lol. this is so sweet. im watching one video a day, and i should be done learning differential equations in little over a month. thanks sir khan!

[doubleja]

"And we're getting a little geeky here" LOL.

[bodymassage]

I don't know how my calculus prof managed to overcomplicate this so much. She should win the overcomplicating award??

[cat0501]

I start differential equations next semester (1/24/11). I think that these videos will be most helpful. Thanks for posting. I am sure I am going to need this as the semester goes on ;-).

[MsWtfisgoingon]

at 04:37 did he say " these 2 constants are just condoms " !? lol

[letmego11]

Now if we take the implicit differentiate of final answer in this video y = 1- (x^3 + 2x^2 + 2x +4 )^1/2, would the answer be the same as the equation

y'=(3x^2+ 4x +2) / (2y-2)? Can some one demonstrate this please?

[SuperKnowledgeSponge]

WTF? 1980 videos? You rock out loud!

[XxMrDudexX]

He sounds so proud at 2:46

[alexspoy]

no word can show u how I am thankful for ur clear and helpful tutorial..... u saved my black a** :|

[powerfury]

okay guys, so a general question about separable equations - when you have an equation such as

(1-y^2)*(dy/dx) = x, then move it to make it separable with the (1-y^2)*dy=x*dx

What are you ACTUALLY doing, because the dy/dx is just a different notation for y', and as far as I'm aware it's not actually a component of two parts (dy and dx) that you can separate in that way.

[FallofDarkness55]

"we're getting a little bit geeky here" lol. well dude, i like geeky style.

[Raphael2885]

@khanacademy you should also maybe in future math vids or if you redo them , at the very end of the last video for each topic you should do rough bullet points of the procedure as the last thing people hear. that would help people grab the idea faster. hearing the bullet points and having some or all of the scratch work still visible would boost hearing the steps and vice versa , you are reading the steps and you are seeing the steps qualitatively and quantitatively all at the same time.

[caml17]

8:48 Just be careful here... -1² should be written (-1)² . If it was -1² that would equal (-1)

[Raphael2885]

@caml17 when the -1 is out front of the equation i have never seen a book write it as (-1)

[TheRozworld]

Thank you for making this concept clearer!!

[Suyamu]

thanks man, I'm a computer engineering student and never liked math ... I will have to solve differential equations next semester again but it's been over a year already since I've had my last math classes so I've forgotten many things already ;)

watching this really helps.

[malachispacewanderer]

You are a baller. Thank you for your humble, wonderful instruction. Props.

[BYMYSYD]

i don't understand. How is "y" a function of "x"?

[sa78223]

@BYMYSYD

idk if ur being serious, if u are...it just means the function y is dependent on the variable x. u should really know that though if your watching vids on seperable differential equations though, thats like elementary stuff lol

[adrasamer]

khanacademy is the next Harvard

[mklvebu]

As always, u rock! Saw you on CNN. Keep up the good work. U helped me through Cal I, II, III and now differential equations (at least the beginning)

[ro890z]

at the end, why is the positive solution eliminated? i thought the initial condition only determines C. yes, the initial condition is contained by the negative function, but y is the union of those two functions. is this only if we're restricting y to be a function and not a relation?

[david0aloha]

@ro890z

If you think about it intuitively the + or - is there because it represents that either the negative root or positive root squared would equal the terms inside the square root sign. The reason that only the positive exists is that, in this case, there's a restriction that tells you what x and y need to equal in relation to each other.

It's like those physics questions in high school where you calculate how long it takes an object to hit the ground, but the solution had to be positive.

[MrDawinz]

you really help me a lot of this subject men...and i like to say that u are lyk my teacher of this subject...hehe

[eltotoX]

I cannot express my gratitude! THANKS A LOT! Cheers! Internets for you! etc...

[ChristianKrabbe]

This is good stuff, very good intro... thanks buddy! I'll buy you a beer if you ever gets to Thisted, Denmark (no you've never heard of it :D)

[gabz777]

Thanks soo much i was having problems understanding but you real good God bless

[imalylime]

thank you AGAIN sal!

[kami645464]

This is 28 times better than my textbook! :)

[bkisme]

You're rendering my calculus teacher (and all calculus teachers for that manner) obsolete.

May the children of the future not be forced to drive miles to an overly-funded institution on a daily basis as we have endured.

Thank you. XD

[heyyhowyadoin]

you and patrick ( the other guy from justmathtuttoring) are young pioneers in the world of online free tutoring. Not only do you guys teach in 5 minutes what my teacher does in 50 but you guys fukn rok at it.

amen bkisme

and thank you sir for these vids.

[orcelb]

Hurray! Thank you!

[hen1588]

Life Saver!!!!!!!!!!!!!!

[silencedfable]

Kind of silly how I understand this better in 10 minutes than the 50minutes in class.

[remsenking]

word!......seriously me 2!!

[liquidstl]

LOL My DiffEQ Professor is chinees, and IM lucky to understand 30% of his english.

[skyfaze]

@liquidstl maybe you are retarded haha

[liquidstl]

@skyfaze If I am retarded because I have trouble understanding his English, then that must mean that the rest of my class is also retarded, because they have the same issue.

[musesparrow]

To Kosekans - it is an operator but if you try some algebra with it, it turns out we can almost pretend it's a fraction when doing this. It's not formal and not technically correct just cancelling things out but you can do it!

[karlkarlkarl1234]

Bravo

[gefallt]

My math teacher Dridi brought me here, there is no other way!

Thanks man, you are great! I will watch them all tonight.

[jayboi54]

"Now I can integrate, and I can integrate in Magenta" ----classic, Lol I have a final in 12hrs....thanks so much

[Kosekans]

I've got a noob question: Can you simply mulitply with "dx". It's not a number, but an operator, isn't it?

[danisjustcool]

yea dude...congratz :D

[metabog]

Who needs tuition fees and university when we've got math books and people like you. Cheers + applause.

[Cathode0]

@metabog colleges are a means of separating the poor from the middle & upper class. They are for the enjoyment of the children of holders of wealth & also a way of tagging individuals as 'of the privileged or elite' class when it comes to employmnt, elect, & wage discrimination. In addition colleges provide for a unique filter on the industry. The minds who make it in are purely the minds scoring well on standardzd tests & rigid performance checks. The common mind passes, else is filtration.

[metabog]

@Cathode0 To be fair, it is really a means of qualifying people according to their knowledge. You wouldn't have someone who only finished high school design CPU's. :P Having a degree in a specific field qualifies you to practice in that field, and hopefully also teaches you what you need to know.

[Cathode0]

@metabog I suppose the education system does have that effect, to "qualify". But CPU design is such an elite position (there being a benevolent oligopoly at mkt) I'd presume that very few fresh college grads qualify for hire given their lack of exp ~Rather those who have experience in microprocessors (like for microcontrolers etc.) Ppl who get into that field are hobbyist though, which endows more technical qualification than graduating

arguemt: class preservation > skill qualification efect

[ATRXXRTA]

@metabog

yeah your diploma

[metabog]

@ATRXXRTA I was obviously exaggerating slightly, this isn't going to completely replace University courses, but if you need math in order to work in a specific field where you're missing a specific concept, this is very very useful .

[ATRXXRTA]

@metabog I do understand the thought of it and support it in fact. but barriers are to hight, real knowledge is never equal to succes or accpetance. for example in an other content for people in developing countries - more realistic in newly industrialized countries, waching/learning stuff is no garantee for something.

but youre right this it is a perfect refresh and backing information.

[movcrit]

@metabog Because putting youtube degree on your resume doesn't look very good.

[IQ233]

Teacher problems? do we all share the same teacher?

[ChevyVetteZO6]

does your teacher not speak english too?

[kanitakhaled]

my math teacher is russian .... and I do not understand a word

[gherre]

Dude, u r a life saver!

[vyaz1]

WOW!! U rock dude, ur awsum...THANK YOU SO MUCH!! (my professor sucks.)..thanx 2 u i'll pass this section 4 sure

[dipsetmeng]

I dont understand why our profs cant just make youtube channels and post lectures on that! Save me the hassle to go to Uni at 8am

[arshie26]

thank you soooooo much my prof is like a 70 year old dude who speaks too softly and writes illegibly. i NEEDED someone who spoke coherently and demonstrated legibly--YOU ARE DA MAN.

[UsdiWalelu]

thank you so much!!!! Hopefully you have a population model DE in here......or a harvesting method that would help me so much right now

[conalnuts]

I started these videos not knowing a damn thing about diff eq's.

I now quite well understand up to this point, and I truly wish you were my professor.

Thank you.

[sameerk88]

yeah this guy is just amazing.

i wish my professor was this good.

[goettemoeller]

Taking an econ class and this is definitely going to fill some missing gaps in my calc memory.

thank you.

[Wurstdesmonats]

Really good vids- Which program do you use?

[kriscivilised]

You are an AWESOME teacher. !

[g1code]

im taking a masters degree now .. and its orgasmic to watch your videos and see how all makes sense !!

.

its nice to see you expanding stuff and learning new stuff from teaching ..for example you dont have to erase stuff anymore as learned to make the black screen is bigger .. and youtube allows u now to have more than 10 minutes vids ..

.

thanks

[Mokash34]

I earned an A on my first differential equations quiz! I worked really hard and I want to thank you! If it were not for your videos, I would've been struggling!

Please keep it up!

[garymarkhov]

KHAAAAAANN! You're the greatest of all time!! Thanks, thanks, thanks!

[daverandomster]

omg awesome, powerpoint video recording.

[spottydog4472]

meh,, think ill go look at some more big tit vids..work on my volume maths............

[mklvebu]

btw, it is cool to get a little geeky

[kb1940007]

on 9:57 why the problem overall added 1 in the first place and what happened if you did it in the explicit form 9:51?

[niklassteef]

Good video! I'm at the moment freshing up my memory about all this stuff and it realy helps to wash this.

Answer to rjm5062:

If you replace you 3*C with C your solution of C is automaticly 3 times bigger then if you haven't replaced it.

Answer to gusphol:

Say you derivate x^3+5 you get 3*x^2. All your constants "disapear" becaus they are no variables. When you integrate you reverse an derivation and you can not know if there should be an constant there and thats why you add C.

[gusphol]

i have to say great video, im no maths head so im just wondering where the hell the c came out of?

[beaner4life]

Wow, you really know how to explain things. I just took a college algebra class and understood what you were doing! (sorta). Although, I don't understand the derivatives because I'm not there yet.

[rjm5062]

why can you get rid of the 3*c and make it just c? Isnt c arbitrary and 3 unchanging? You dont know what c is yet, but when you do dont you have to multiple that by a factor of 3?

[novatodeguitarra]

c is a constant that you add to the solution it does'nt matter it's value if you don't have an initial condition it's just c it means thac you can make it any number you want and it still will be a solution

[00GameMaster00]

"I can integrate... In magenta..."

Great video :D

[kriptonboy]

awesome dude!!

[algorithMIT]

Sal obviously went to MIT for math

[enaba2006]

You are a hero in a real special way! May all good blessings come to you, and aura of good karma surrounds you! :-)

YOU ROCK!!!!

[l337skater]

ok then

[victorgimenesfraga]

thanks!

[driftx2]

godly. you are my hero!

[haider87]

Awesome!

[C1t1z3n3r4s3d]

love the added enthusiasm when you near the end of the video

[Donk696]

As soon as you multiply through by dx you turn it into a cookboox method and are not working relative to theorems or principles. Just integrate wrt x and use the chain rule for integrals to get an integral wrt y.

[wigglebytes]

I'm afraid I have to agree with this person. At 2:33 you resort to one of the things that helps make calculus so confusing. Misleading shortcuts.

[ComplexSuperiority]

you've run out of time? lol

nice video

[esnorgomez]

dude that was great, i now know how to solve these things

[electriciansmate]

Your giving differential equations a bad name, your making them too easy; keep up the good work.

[arwindeboer]

Great explanation! Thanks a lot!

[Savware]

This is a big shout out from an Engineering Student in India...You are the man...Keep up the Great work in the pursuit of a knowledgable world!

God Bless

[moaninglory]

u're the man!!!! and every uni professor I've come accross should be stoned to death or hung u just showed us how teaching should be done

[secondwheel2]

i agree

[dannyboy12357]

very clear and thorough explainations 5 stars

[nhojmabon]

Thankyou very much, your videos are very helpful. 6 stars.

[totlolrofl]

Very nice - thanks

[dave597]

Thanks. Like the simplification at the end! :)