Differential equation introduction | First order differential equations | Khan Academy

Practice this lesson yourself on KhanAcademy.org right now: www.khanacademy.org/math/diff...
Watch the next lesson: www.khanacademy.org/math/diff...
Differential Equations on Khan Academy: Differential equations, separable equations, exact equations, integrating factors, homogeneous equations.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to KhanAcademy’s Differential Equations channel:: / channel
Subscribe to KhanAcademy: kzbin.info_...

[@MrPerry435]

"I'm assuming you've had a go at it" Quite bold of you to assume that Sal

[@matthewlefaivre8975]

Sal: So I'm assuming you had a go at it... Me: What's a derivative again???

[@kornelkr6639]

😭

[@epicmatter3512]

If you think of a tangent line, which is a line that touches a function at exactly one point, and is really just the limit, both the left side and right side of a secant line, has a rate of change, but is also the rate of change at that exact point. So all your doing is finding the rate of change or more simply rise over run. And these lines are based off of circles, and limits are based off the simple difference quotient, which in itself is just a way to think of rate or change. So all this is, is complex forms of math built off of circles and rate of change(rise over run). And a circle is just based off the idea of a closed loop, and is something people just drew, and rate of change is just the idea about how numbers change over time in a simple linear equation, which is based off of the ideas of numbers and variables, which in itself is based off of the idea of numbers.And a circle is just geometry, which is also based off of numbers. So when you get down to it. ITS ALL JUST NUMBERS! And differential equations are just ways to relate certain functions like derivatives, but actually can relate the world to numbers. ITS ALL JUST NUMBERS!

[@epicmatter3512]

@@kornelkr6639 I got you.

[@angelfalguera9199]

just exactly what I'm experiencing rn

[@rendodge7884]

its also important to understand the anti-derivative

[@jeffreynorman5221]

As a student learning differential equation but no textbooks provided in the class, these set of videos means everything

[@aominetaiga343]

No offense but how in the world can your professor lecture differential equations without providing texts?

[@josephruvelas9592]

@@aominetaiga343 probably a school with common exams. math department likely has a curriculum and material to teach/ adhere to but i agree, its kind of unheard of. there probably is a textbook tbh lol

[@Podzhagitel]

z-lib

[@momouwu1937]

@@aominetaiga343 It's kind of normal especially if you are doing an exam specific to a particular developing country and the curriculum isn't the same as the Western countries. You just don't know what textbooks to use. Like if you do SAT exams you know you can use SAT textbooks and if you do A-levels, there are A-level textbooks. Still, if you use other textbooks, it can be helpful.

[@Meimingming]

@@aominetaiga343 mine just gives us exercises but we have no theory about it😭

[@walletinsiders]

He says "differential equations are super..." My brain is like "EASY??" ^_^ then he says "Useful" -_- Useful stuff is hard bruh

[@sunitadas8068]

Ikr 😂

[@kinglaserna1533]

Useful? I’ve been learning Calculus since August of 2019 and still have yet to use out side of school

[@leowu1644]

King La Serna When you get a job in STEM them you will.

[@cardinality1975]

@@kinglaserna1533 Surely you've been introduced to some of the applications of calculus? There are a million ways it can be useful, very interesting stuff!!

[@UltimatePrinceofBB]

They are very useful depending on what profession you'd like to take. Calculus is very crucial especially on probability, and there are a lot of professions that requires being good at probability. For example, being an actuary, or having a job at insurance companies

[@charleslucas1784]

The main thing that I like about the Khan Academy is that he makes advanced math that's usually difficult, a lot easier to understand to where anyone can learn and master what he's teaching.

[@maxarmstrong885]

A great video; I was highly recommended to watch your vids to improve my maths and I have to say you are great at explaining things. I look forward to the whole series of differential equations being this helpful! Many thanks

[@mikemustmurder]

I'm pretty sure I'm going to fail this class.

[@emilielee3378]

mikemustmurder pretty sure that i just failed my final exam in three months :')

[@darnelross6357]

did you fail?

[@hman2875]

@@darnelross6357 i guess so

[@islamzerrougui7718]

did u fail ..??

[@angelinebantillo3128]

I'm curious. Did you fail?

[@user-zg4sn5jo6v]

Finally! a new playlist for differential equations, I've been waiting for a year.

[@fusion9619]

I'm starting my new years resolution a few months early : watch Khan Academy every day.

[@buddychumpalfriendhomiebud9242]

How are you doing with that?

[@fusion9619]

@@buddychumpalfriendhomiebud9242 hmm... started strong, then forgot. Good timing!

[@soraxinmediares4494]

@@fusion9619 good luck man

[@SV42165]

Why?

[@kwasipoho]

Mine this year

[@toby9999]

After watching a truck load of introductions to differential equations... finally one that makes sense!

[@gimonoko]

When I hear Sal's voice, I automatically listen. I automatically want to learn and understand the lesson. From the years I've spent on khanacademy, he has become my everyday professor/coach when learning. I'm studying electrical engineering right now. Khan academy has its own professor in that department, but when whenever I go back to whatever Sal's teaching, it makes me feel happy to hear his voice.

[@zeroseven51]

Love the way you explain each step Easy to understand Keep up the good work

[@jordanmathewbailey]

your videos are by far the most helpful!

[@akshaypainjane2094]

You are doing a great stuff by spreading education! Hats off!

[@joshuangtseung6948]

I used to watch these vids for GCSEs I'm now doing an undergraduate and I'm still here, who says KZbin is a waste of time smh

[@rocketpsyence]

This is a good refresher so far. Took diff eq ages ago in college and always felt depressed that it was one of those use it or lose it things and wanted to try and get it back.

[@MaximQuantum]

I just figured out a great way to study math at school: Watch videos on the topic to get more insight, intuition and curiousity. This is definitely one of the elements that modern educational systems lack, namely recommending great youtube videos!!!!

[@tbpom1003]

thanks for the video! I'm taking a differential equation class, and my teacher skips all steps. Now I know what's going on lol

[@jackandonlyjack3268]

Teacher skipping steps? I guess it's time to skip your teacher's class.

[@impooser]

So simple and straight to the point. Thanks.

[@angelakate9922]

I still need to watch this again a couple of times. Because the information just easily flew out of my mind the first time i watched this.

[@nightt2040]

I’m currently a sophomore in algebra 2. All I wanted to do was take a sneak peek of what math would be like next. The only part I understood was when he showed the algebraic equation 🙃 what is math

[@katiakominski432]

Hey, not a bad idea, but you took a bit of a leap here :D You might want to look over (limits and) derivative calculus first, and then you'll understand this a bit.

[@ThatWasherNerd]

hahaha I have a calc AP test in 6 days and I don't even know what this is.

[@comprehendnature2404]

In addition to derivatives, you will need integrals and limits to understand differentials. Without them differentials cannot be understood.

[@alexia8511]

CE student here, and I'm also taking a sneak peek of what's coming.. :'>

[@datmo0se992]

WHAT IS MATH?! TEACHER DONT HURT MEEEE DONT HURT MEEE NO MOREEEEE DUN DUNDUN DUNDUN DUH DUH

[@xogmaster]

Sal: Here's a differential equation. Figure out if one of the solutions in this list of possible solutions is the solution. My professor: Here's a differential equation. Good luck idiot!

[@Jessica_Jessica_Jessica]

This was a great introduction! Thanks!

[@ignantxxxninja]

very nice introduction.. I'm reading the preface of the textbook before the semester starts, and it seems like this is going to make sense.

[@zihadhasan7492]

This discussion is so much live. I mean this discussion has a life to make us understand.

[@alassansaine]

This is an amazing introduction to differential equation. I am taking the course this year.

[@Mathefusions18]

Straight to the point explanation. Good work..

[@blockbusstar]

This is the second order differential equation

[@hahaha-zi1xf]

what is the difference between the first order and second order?

[@alesolano9081]

@@hahaha-zi1xf the order corresponds to the bigest derivative in the ecuation (if it has a second derivative then its a second order differential ecuation)

[@austinpundit6321]

Sure, but he was just talking about what a differential equation is.

[@dxalrado]

@@austinpundit6321 look at the title and say that again

[@toby9999]

@@dxalrado He's just talking about differential equations. It's an introduction. We don't care about the order yet. The concept already difficult enough without it.

[@amutuhaireeliza8767]

This has been my best introduction to differential equations ever🙏

[@ikesteroma]

Your handwriting is excellent.

[@patrickoloo241]

that was really useful

[@beepnw3659]

the Grad student that teaches my calc class didn't go over defferentials at all in lecture and then proceeded to put it on the homework. Thank you for saving my grade.

[@drmksu38]

thank you Mr kahan .. i cant do anything without your amazing channel ♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

[@seanspartan2023]

Thank you for this. I managed to get all the way thru university and get my math degree without taking a single course in Differential Equations. At the time I didn't care because my work only involved theory, but now I regret it because I'm more interested in applied math and physics...

[@AlwinEmmanuel-S]

I rlly love this and i am actually understanding this... even tho im in year 6

[@joshuaaustin2541]

that silent chain rule you mentioned helped, i laughed 'cause indeed the derivative of e^x is "1" e^x and will repeat in the 2nd derivative. gonna stick around for some more khan videos, prep for college and first at math is differential geometry, this video is just 1% of the entire math146

[@earllabule4349]

looks so hard, but actually so simple....*Mind blown!!!

[@clyt9636]

Thank you!

[@walktroughman1952]

Many people I know hate differential equations, idk I love them to bits, I find them fun. I thought I'd struggle understanding them cause I had struggled with calculus, but it was a surprisingly smooth ride. They really are pretty fun to deal with. _Unlike the spawn of Satan that is probabilities and statistics._

[@theinfeno]

I really appreciate that these lectures explain everything in simple words, don't skip any steps, and do not talk down to you like you are stupid.

[@nathaniel4146]

Iam about to take this subject next sem! wish me goodluck! just starting to learn... Imma update you guys how I did after this incoming sem. BTW, Im a CE student from Ph. Best of luck also to those engineering students! we can do this!

[@XDXD15644]

Best of luck. Im gonna take this subject too. IE student from ph.

[@itzyryeji3164]

Bruh i’m grade 12, and planning to take ece, we have De this sem uwuuu from philippines too

[@snullahc13]

so, how is the course? I also consider taking DE next semester...

[@Engr.S-Jay29]

Im an ME student from Philippines. I have my Calculus 1 this semester.

[@waltercatapang7159]

Same wd you bruh, God Bless Us

[@jaimedelapuente349]

THis is the BEST video explaining DE, it has finally made me understand them. Thanks a lot :)

[@johnthegamerman404]

Power series expansion method is my favorite way to solve a differential equation

[@jef1ferys]

swear this is second order, not first

[@JonpritPritam]

thnk you very much sir

[@stvp68]

Nicely explained!

[@kispangit3912]

Wow. Finally I know now that the solution of diff.eqs are functions. Gee! Good job! A math mystery finally lifts! Not that I can solve any, haha!!

[@itsboshd]

WHERE DID HE GET e^-3x FROM???????????

[@semiawesomatic6064]

srmorales08 I know this is old, but I ran through it with a general e^ax. You end up with a quadratic who's solutions are 1 and negative three. I'm sure there's a more consistent way in another video you've probably already watched, but whatever.

[@AkashDasYT323]

from Arab

[@elenav1210]

I'm 3 years late but I'm just studying it now. He got it from l²+2l-3=0 Where l² is d²y/dx² l is dy/dx and y is just 1 From there you get -3 and 1 solutions for l.

[@Gypsy_Danger_TMC]

@@elenav1210 Yes just realised you're right. He's used the auxiliary equation

[@R4G3QUI7]

very good!

[@Velas99]

Amazing explanation

[@musicrainbowheals4537]

Very clear and simple introduction of "Differential equations" 😊👌

[@jamiainaga5853]

Khan Academy knows everything

[@sarahrashed7648]

I got it. thanks!

[@jasdrawssometimes4660]

i wish there was highschool college where you would take college courses on a highschool schedule. so like an hour- 2hours a day, everyday, for a year. i would be so good at differential equations. i wish i had the time to love math the way i did in highschool

[@duckyoutube6318]

Wow this is amazing.

[@Aisyah-qf2pz]

Thank youuuuuuuuuu.

[@thezero4546]

good job, Thank you

[@thatnibba2551]

This is helpful

[@jonaskoelker]

One thing that annoys me about differential equations as they are often presented is that they omit specifying what's a function of what. What helps me keep the eye on the ball is this idea: When solving a number equation, like x^2 = 4, you're really describing the set { x in R | x^2 = 4 }. One description is to list all the elements: { x in R | x^2 = 4 } = {-2, 2}. When solving a differential equation, you're describing a different set, such as the following: { f: R -> R | f'(x) = f(x) for all x in the intersection of the domains of f and f' } or { f: R -> R | f''(x) + 2f'(x) = 3f(x) for all x in the intersection of the domains of f, f' and f'' } and so on. I have a proof using only ideas from my one-semester real analysis course, without Taylor series, that if f' = f (where f: R -> R) then f(x) = f(0) * e_x where e_x := lim (1+x/n)^n as n -> oo. In other words, { f: R -> R | f' = f } is a subset of { f: R -> R | f(x) = f(0) * e_x for all x }. I have only proven that f(x) = f(0) * e_x is a constraint that can be satisfied if f(0) = 0 [implying f(x) = 0 for all x]: I have not proven that non-zero solutions exist, only how they must look _if_ they exist. This is a less precise description of the set { f: R -> R | f' = f } than I would like, but it's a start.

[@jinmingtang1545]

I need to review the chain rule of derivative to understand the calculation.

[@rokettojanpu4669]

All it’s about is dealing with derivatives of a composition of functions, i.e. functions wrapped inside other functions. If you’ve got a function of x like f(g(x)) then the derivative is f’(g(x))*g’(x) Example: Derivative of (sinx)^2 = 2(sinx)(cosx)

[@Bigsneaks818]

I’m going to ace this class fr

[@sujanjirel5456]

nice video sir..nice explaination

[@Sharna0321]

Why is your voice oddly so good...

[@nodiyaa158]

Ikr!

[@noimosyni_0594]

thank you

[@cristianortecioesteban]

Thanks, done watching.

[@jinoymathew440]

Thank you very much

[@SilentJnation]

Boom! Mind blown.

[@uvideos6795]

I have a request. Can you arrange the playlist by what order to watch these please? Thank you very much.

[@TanushAdithiyaBEC]

Simple and nice

[@theomiado7954]

this is going to be a bumpy ride

[@Jako4460]

Thanks

[@zzing9nuna]

thanks to make this video

[@sultanwiranatakusumah4154]

Thankyou sir

[@fadhilahrafifpahlevi9166]

Does the y should be exponential to solve differential equations?

[@rr.studios]

Mistook this for ASMR for a bit there.

[@soniakhan4657]

thanks

[@davidfarquharson8207]

Thanks bro. 🔥😎

[@audiomac]

Thank you. I was so confused when my professor was teaching this because I thought the second derivative was an 11th power lol.

[@transgalactic]

Yes it checks out, but how did you arrive to the solutions?

[@AbiM-G]

you divide the digit that has the y or x by that number and then simplify both sides

[@AbiM-G]

you understand 5x means (5× x)

[@AbiM-G]

eg 3z=6 so 3 3 then simplify ,then you will be left with z=2 so that means 3×z which is 2 is 6

[@cristimarius3940]

neat... thank you!

[@suzakukeen6703]

Gm cristi im having some probz can you help??

[@cristimarius3940]

@@suzakukeen6703 let me try

[@nwjt]

what software and hardware are you using to write with? it looks nice

[@aslakskailand2589]

what is the software is he using to write?

[@TheRayll]

paint

[@babitashuckin5831]

@@TheRayll no... It's not.

[@purvai4701]

Classic khan academy stuff its iconic right?

[@nityavyshnavimadduluri3568]

Hello guys ! I guess there's some problem in the audio files for the videos in Khan Academy app.The audio file here is super clear compared to that of the videos in app.

[@vivianmader4523]

hi bestie thanks for the help. love ur handwriting.

[@zevil1999]

Thank you

[@davidbosilj]

may god help us all

[@wetwillyis_1881]

I’d be lying if I said any of this made sense to me.

[@hambooger6117]

civil engineering student here studying differential equations from scratch! will let you guys know how everything goes for me

[@kevindemeulenaere1459]

you didn't

[@hambooger6117]

@@kevindemeulenaere1459 on my 3rd year of college and i still dont know jackshit

[@kitchemk]

Nah I watched a video that just made all of this very intuitive

[@Healthsolution.694]

great video

[@alishaiqbal5105]

Sir if existance and uniqness fail in ODE than we use numarical method?or we have some other method to solve ODE?

[@dsi2867]

What program do you use to make these?

[@sagargurung8682]

what is the app you are using?

[@josiahswanson5518]

There exists a set of an infinite number of solutions to an ODE. Reply with an equation that satisfies the above statement .

[@Shuforces1]

A question, are there any lectures/materials that I should look at before I look at this? At 4:08 I have no idea what he is asking me and how I am supposed to do it.

[@AWESOMEDAVIDPOWER]

You should look into derivatives. He y' is the first order derivative of y, and y'' is the second order derivative of y. y in this case is e^(-3x). To learn how to find the first and second order derivative of e^(-3x) make sure that you learn the chain rule part of derivatives as well :)

[@brandonkoh4544]

Deeper

[@shivangi3030]

Why do we eliminate arbitary constants for forming differential equations

[@giulio665]

what are you using to write.

[@_valles3438]

so, is the solution typically involved with some form of e^x??

[@okleymensah1727]

Please where and how do I get the continuing of this video

[@purvai4701]

On the khan academy app or website