What is a differential equation

[@lordgerth9046]

13 years later im learning from this man

[@omarrazibaouene8156]

15 years

[@laura_22]

me too @@omarrazibaouene8156

[@MathswithSunnyspbpu]

@@omarrazibaouene8156 16 years

[@az_earth]

16 years​@@omarrazibaouene8156

[@Taylachteam]

@@omarrazibaouene8156 16

[@abdullahabdelqader16]

Mr.khan , you deserve a Nobel prize for your magnificent help to students from all over the world. You are truly the father of all teachers.

[@illumiseo123]

I remember this guy teaching me chemistry in college. Now he's teaching me math 10 years later. Super cool.

[@lutherhoward7637]

Hopefully, you paid attention and made an A.

[@venkatap.2463]

Holy moly, I spent the last few hours trying to figure out what the purpose of DIfferential equations and this man answered it in 11 minutes. What a legend

[@detleftibax]

Man, you're like the guy everyone hopes to find in mathlessons: crystal clear explanations, language that makes sense, good examples...You're helping me out time over time. Thanks for sharing your knowledge man, I really mean it

[@dogewisdom9921]

Had a middle aged Chinese teacher in college. Probably the best I’ve ever had. Despite barely understanding her with her accent, she was legendary in her teaching

[@jarratt51]

damn didnt think this guy would still be helping us 10 years later

[@surfingcipher1059]

16 actually

[@generichuman_]

@@surfingcipher1059 16 and one month actually

[@StephenCurry-ff4zc]

One thing I like about Sal is that his aim is to make you understand a topic intuitively. Patrick on the other hand, gives u an equation and teaches you how to use it. Not saying Patrick is bad, I love that guy but if I had to choose, in the long run, Sal's method is the best

[@aseelworld3359]

Agree

[@dhilrukshanpradeep7265]

14 years later and I am using this man's videos to teach students

[@alfredvalentine4584]

15 years later I'm using this videos to learn...

[@Hammadisteachingchemistry]

15 years layer still learning from this man

[@tallkekepink95]

I am now a sophomore in Mechanical Engineering. I am taking Differential Equations at a Univeristy and I never ever seen this stuff in my life. I have already taken Calculus 1 and 2. I skipped 3 because the class was too full... Any way I just wanted to say Sal your videos are very, very helpful!!

[@evrythingelswastaken]

Learned more here than I did in 2 hours at school. Thanks so much!

[@ROXcursed]

This guy is an absolute hero. If you'd taken the time to see his later videos you'd see the quality improves dramatically.

[@breyvbienfu2728]

THANK YOU VERY MUCH TO THIS VIDEO! I'm in tears. I missed the first two meetings of my class so i have to do a self study about the whole first chapter ; - ; I couldn't understand a thing! Thank God I found this! Bless you!

[@lindorchocolate]

Sign of an amazing teacher: I'm a junior in high school (16) and I understood everything you said in this video :)

[@GETurnt]

we learn this is high school in India, and I totally understand that you must be 24 years of age by now. yeah, I'll go...

[@raidernathan4209]

Also currently a junior in highschool (16)!! 😆

[@kyokushinfighter78]

I learn more by watching your videos than attending Diff.Eq class taught by Oxford grad professor for one goddamn semester! thanks, keep up the good work...

[@RoYaLMarTineZ]

5 stars, i admire you for trying to teach people some of your knowledge FOR FREE!!!

[@vtgaming9204]

Man i am fucked. I don't know how i passed first semester maths

[@princesinday6570]

hahahahaahaha well done buddy, well done!

[@edsonacarapi6932]

I don't know how much money this channel is making from these videos but it's not enough. Thank you Khan Academy!

[@user-vk2cd9qw7i]

It's a 501c3, you can donate at khanacademy.org

[@cookingfeveraddict]

15 years later and still useful

[@William_sJazzLoft]

Brown you explained it as well as I could understand ( which is reasonably well). You explained it like a pro. And judging from your discourse you seem to have no problem defining the nomenclature. The distinction between linear and nonlinear is where I run into a little bit of difficulty.

[@LipiKatiha]

240p, we meet yet again!

[@HawkarAli]

i dont know why he does not upload in a high quality it is 2014 :/

[@LipiKatiha]

Yeah maybe he thinks this is sufficient

[@eazymoney3055]

Hawkar Ali I think its because he posted this video in 2008

[@bedresamarth]

@@HawkarAli he did

[@omarmagdyahmed4259]

hes writing theres no need

[@aritrachakraborty6942]

this man is really awesome and he knows everything maths , physics, chemistry

[@saria3094]

I'm in my last year in high school and I'm blessed with this explanation. Thank you! Greetings from Sweden

[@chimwemwegerald8745]

Where are you?

[@TheBalisto]

You are so incredible that you have 2044 videos of free lectures! You are the most knowledgeable person ever! And, extremely generous for doing these videos! :)

[@peteradawson6576]

"The language of science is mathematics" was said by Galileo 400 years ago, and he had a point. One cannot describe something in nature unless one can measure it adequately. And Calculus helps to tell us how to describe the relationships between things that change.

[@jimcar53]

i don't care what the others are writing, but at least i finally understand differential equations. thanks very much.

[@mirindada]

learning from him after 15 years

[@Eudaimonia239]

thks a lot man, a lot of people here at home start looking me bad because i was seeing this, but its really great cause i have an exam on tuesday so thanks a lot.

[@gdullard]

this 45 video playlist is gonna make me crush this exam

[@j2011j2015j]

My professor for engineering math gave me this link along with one other video to watch before class. This seems like a fairly good preparation video

[@ARYT13]

This guy is actually better than MIT's ODE lecturer.

[@haal001]

Wow. This guy is awesome! Definitely much much better than my instructor. Thanks for saving my life.

[@dasuperfly007]

Keep up the good work khan, man I can't imagine quiting my job to help teach the world but you did it. And I appreciate it.

[@daltonwilliams6297]

Just started differential equations, this helps. Wish me luck lol

[@pebblepod30]

Dalton Williams Good Luck =^)......though that was 6 months ago!

[@daltonwilliams6297]

Platypus Paws came out with an A! Had like a 99 average!

[@henrycoldrain8151]

gl

[@sidrahnaeem9234]

@@daltonwilliams6297 Tips please. Im taking differential equations now.

[@daltonwilliams6297]

Sidrah Naeem just study a lot!! Don’t be afraid to ask for help when you need it. Don’t give up you’ll be fine!

[@Mermaider]

yah i see people have already posted good comments so I will keep mine simple. I don't know what you believe in but this work your doing might get you into heaven. Thank you like you like can't imagin :)

[@crzzyguy]

Never thought of maths being so COLORFUL!!!! Great videos, keep up the good work!

[@hotrokr69]

Im only in Algebra 2 and i understand this! That's how good of a teacher he is! (I Can't wait for Calculus!)

[@dejvi997]

If I get diploma from faculty, I'll give it to you because you learned me almost everything.

[@adityapasari2548]

*taught XD

[@m2moun1]

he is better than my teacher in uni ... brilliant

[@jauneliss]

why can't lecturers be like you? thank you for all tutorials.

[@colorsendinginurple]

wow, everything that i've learned in the past month of MA 341 just clicked into place. Thanks!

[@tadm123]

Brilliant video, can this man get a nobel price already?

[@ruiwenguan2640]

Thank you for the clear descriptions! Now I finally know what’s going on in last quarter 🤣

[@021jaguar]

my lecturer must learn from you about the methods of teaching.

[@MissBee77]

this was a good intro [which my professor just completely skipped]... at least I know why I'm supposed to solve these and what my solution means... Thanks so much!

[@drrojas]

This might be the 100th time I COMMENT a vid of you saying : "IN KHAN WE TRUST!" Youve gotten me past through Calc 1, 2 and 3 , Physics , and now Dif. Equations... class starts Monday , but at Khan academy CLASS STARTS Whenever I feel like , 3am thursday night? YES!!!

[@alexxstryker]

this has totally put me in perspective of the huge ifrastructure of functions from calculus to help derive the correct standpoint of the whole discipline....

[@ahonsarkar]

Thanks to these lectures, I KHAN finally do Differential equations. you rock.

[@Zodiacpoom]

I love you man.. I am studying to electrical engineer, and what I have learned in just two of your videoes is more than what I have learned in almost the entire semester :)

[@TheKFUPM]

that was a clear simple free lesson thanks Khan

[@mrhnm]

Watching his videos allowed me to go from middle school level math to intermediate college algebra

[@damjantasevski5769]

10 years later and this is still helpful

[@maxvikstrom9350]

The problem is not to simply learn how to find a soluation but to apply them in practice. 90 can find any degree IF the derivate to a function but not 90 percent understand why they are importent to describe a function

[@someguy2885]

75 years later and I still come back to this video 👍

[@saimqazi1663]

16 year later i am learning from this man

[@Sinusis]

very clear explanation. good teaching skills. thank you.

[@AThomasKent]

Sal, I love you (and your team). Thank you very very much for providing this content for free! :-)

[@alexr1212]

thanks for breaking it down and making it simple to understand

[@AntKPro]

I watched the whole course. Thanks a lot. Very understandable

[@EvelcyclopS]

God I'm fucking dumb.

[@JebediahsLab]

Don't worry about this kind of math unless you are going into engineering.

[@EvelcyclopS]

+Jebediah's Lab mate, I'm in fucking engineering!

[@cherryxx6070]

... now I am scared.. I am going to take engineering next year *_*

[@JebediahsLab]

Lu Lu Just study. Don't party and do stupid crap, be diligent and you will make it.

[@cherryxx6070]

+Jebediah's Lab Thanks for the advice :) I'll study hard

[@druebwake]

im in 4th year electrical engineering and i still dont understand D.E's lol...this has helped heaps thanks

[@Monaworld2023]

I just found out 45 video of DE Thank you, it helps a lot,you are so great!

[@abaddon1112]

Really makes you rethink the entire education system, doesn't it?

[@RVCata]

Got a final base on this differentia equations 2 days from now. Im sending this guy a fucking truck of beers. This is so helpful.

[@Person514cs]

very informative. We need more people like you.

[@ky1esty1e]

You teach us Physics AND calculus?! I love you dude!

[@kypronite]

Lately I wanted to learn differential equation badly and I have watched almost all your calculus video.and I didn't see any differential equation video in your playlist except for 1 video. But today i open the playlist and I saw one of the title ,'Differential equation' Imagine my delight =D

[@princesinday6570]

OK. I will start from here this instant and will try to finish everything. I badly needed this one!

[@erdwaenor]

It's good job, thanks for sharing such important information. But I could only understand the explanations after finishing roughly 1 semester of Differential and Integral Calculus initiation at my University; before that, most information on the video wasn't clear, or was in a explained in a way too advanced level jumping important Calculus fundamentals for the initiates. But now (after 1 semester) however, I can grasp the ideas on the video quite well; and it's very useful.

[@goodgoodgoodful]

Sometimes subconsciously I feel like to scroll up the video :) BTW, what a great and colorful lecture!

[@leopoldbirkholm]

Thank you Khan Academy for making this video. Funny thing, I won't need this on the program I want to go. This is just something I need to get the grades to be accepted to the program. =)

[@coletrain3162]

This is going to help so much this term.

[@harshavardhan816]

Can you do videos on Tensors and tensor calculus?

[@netninja90]

Thank you. This was very helpful for me trying to understand the concepts in my Calculus 2 Class.

[@RoyalSapphireMods]

My teacher taught me this one concept for two months and it never made sense but I watch this and I actually get it

[@peteradawson6576]

dy/dx represents the result of differentiating the function y(x) with respect to the independent variable x. The multiplication by dx is part of the integration of dy/dx with respect to x which recovers the function y(x). Integration and differentiation are inverse operations as proved by "The Fundamental Theorem of Calculus". Hope this helps to answer your question.

[@sam222ist]

Thank you so much! you are a very nice teacher. best regards from switzerland!

[@alastairzotos]

I wish I had you as a teacher.

[@aari8350]

Omg thank you Sal, you've cleared up the dy/dx confusion I was having.

[@rolo928]

x^2 (d^2y / dx^2) + 2y + blah = sinx This equation is linear because the independent variable, Y (the variable being derived), is to the power 1. The (d^2y / dx^2) shows its a 2nd order DE. If X was being derived or if you saw a X' or dx / dy then this equation is non-linear. Hope this helps.

[@92310CAMILLE]

wow,a better preparation for my incoming lecture in D.E.

[@drif7walk]

BUT WHAT DOES IT ALL MEAN?

[@karlmorrissey8845]

I'm with you man

[@jimkeller3868]

Don't expect very many math teachers to tell you what it means

[@berni2905]

I don't understand your question

[@benitomunoz8661]

@Hussain Mustafa applause

[@chaoticstorm8145]

Watch 3blue1browns video on DE. He does a good job of explaining

[@dmt1994]

You should make a video for differential equations, that splits the differential up and solves it as a system of equations! My teacher is grossly unhelpful. Thanks, and Great videos!

[@immortal6699]

WELL DONE....U HELPED ME ALOT

[@alial-musawi9898]

I'm a grade 12 going to university next year. I'm pre-studying this stuff, and thanks to Khan, I may get a very high GPA! Well, I'll need it to keep my scholarship, so thanks a lot!

[@irenerubrico2300]

It's great it really helps me

[@mono7891]

Good explanation! Linear and non-linear can be defined as constant and varying slope.

[@edtechrwanda6282]

better than my lecturer!i like you mn

[@wildrider100]

great vid frm a great teacher

[@redbuthotter]

I agree, very helpfull. Please do not listen to the above comment. Coloured ink on a black background is superior to black text on white. Why are all major CAD programs coloured lines on a black background? Because research has shown that black backgrounds reduce eye strain and are more visually clear. Also, you can buy a tablet pc for less than $200 but is really not necessary in this case. I am very impressed by the readability of the text.

[@cochisewolf]

Thanks for posting this, it's been a great help!

[@sammcewan9544]

So in the example he had you can easily find solutions by first solving as though it were a quadratic. Y^2 + 2Y - 3 = (Y+3)(Y-1), therefore from the quadratic Y= -3 and 1 are solutions to the quadratic. In the differential equation this is represented by raising e to these powers. Therefore the solutions are e^-3x and e^x. I'm still at school, but seems like it works

[@hokieboy01]

You are correct. Though the solution as a single equation is y=c(e^-3x)+b(e^x) with c and b being constants (at least for the general solution)

[@uthpakhi]

12 Years later, Here i am learning Differential Equations from the Super Man Sal Khan.

[@Mrsaries94]

my prof is english and he mumbles. Thank you fr this

[@johnwroblewski6458]

What's interesting is that any linear combination of those two solutions is also a solution to the equation. And conversely, any solution of that equation also must be a linear combination of those two solutions.

[@rxgntz]

Thank you very much! ! Your explanations are great!

[@nucleartide]

thank god for people like khanacademy and thenewboston.

[@TBlev215]

Yet there are some schools in America who are using this system in their own classrooms. There is still a small hope that other schools will eventually catch on and revolutionize education in this country. Just need to give it plenty of time...

[@damisimsanii544]

woow this video has a million views...nice