Laplace transform to solve an equation | Laplace transform | Differential Equations | Khan Academy

Courses on Khan Academy are always 100% free. Start practicing-and saving your progress-now: www.khanacadem...
Using the Laplace Transform to solve an equation we already knew how to solve.
Watch the next lesson: www.khanacadem...
Missed the previous lesson?
www.khanacadem...
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: www.youtube.co...

[@echow2001]

bruh i just realized that when he is 'out of time' he was literally out of time because back then yt has a 15min limit.

[@nitro361]

The more I know

[@louist103]

at the time this video was made the limit was 11 minutes.

[@maximussamir2332]

I know Im asking the wrong place but does anybody know a way to log back into an instagram account?? I stupidly lost my login password. I appreciate any assistance you can give me!

[@matheuschaves3468]

15 years later and Khan Academy is still saving my grades gotta love it!

[@djsiuafkjghdsjfhkdsl]

Dude, you the real MVP!!

[@eduardedwin]

I like the way you said about your writing space as 'real estate'. Hahaha... Great video. Wish I found your video sooner. My Diff. Eqn lecturer was crap.

[@MrZeus7]

@ardotadot This series really is very, very similar to the Fourier Transform - watch these videos and whenever he mentions "s", replace that with "jw" or iw, whatever you use - imaginary omega. The 's' in the Laplace Transform is a + jw (the a is some greek letter, I forget). The Fourier transform is basically when a = 0. Hope this helps!

[@nidhinsathyan6904]

It's the best class I attended about Laplace transform.. I like your simple examples and clarity of illustration.

[@kweweli7821]

The professors are not worthless.Watching a video has its own advantages-you can pause, replay,forward when you don't get something. Moreover, professors have to cover a lot of topics and they won't spend the class time solving a problem. Professors have to teach many classes and grade papers nearly on a daily basis unlike youtube video developers (can upload videos anytime at their will). Most people only turned to a youtube video when they don't understand their professors or the text book-meaning they already have a previous knowledge on the material before turning to youtube. This is the same advantage you have when you read your textbook before attending lecture.

[@famguy218]

Well my professor and TA are Russian and Greek, and I'm American so it's hard to understand them (which shows how many Americans are pursuing PhD's). Sal Khan is evidently American so it's much easier to understand him and he's actually a good teacher, too. Lots of college professors (at least at U Minnesota and U Wisconsin) aren't that great. I learned better from my calculus teacher in high school.

[@kweweli7821]

famguy218 ooh, I understand your frustration.

[@AS-fm5ew]

+famguy218 salman khan is not american...he is indian...

[@famguy218]

Ashish Sandhu He was born and raised in America

[@veggiebot8855]

professors are also being paid to do it and I am not paying 9 thousand a year to khan academy so I don't expect regular uploads.

[@Default_089]

Its great for understand the concept but it takes too much time if you have 20 of these for hw ahah. (note that exponent in the form ^(4) means four prime or fourth derivative rather than y^3 which is y to the third) Heres what i do. y'' + 5y' + 6y = 0 s^2[Y(s)] - {s[y(0)] - y'(0)] + 5[sy(0)-y'(0)] + 6[Y(s)] = 0 plug in initial conditions since you have y(0)=2 and y'(0)=3 simplify and take out Y(s). initial conditions will be moved to the right hand side of the equation. get Y(s) alone so divide. now you have to seperate by partial fractions. try to simplify as much as you can. finally take the transformation after finding the constants and fractions. overall great for concept, always try to narrow things down

[@zgr9]

cool, good explanations i like the step by step procedure, so many math professors neglect the small details in explaining things

[@aidskeys]

This disembodied voice is what's gonna get me through this exam..

[@samiastsegay512]

your explanation is way too good!!!! Gob bless.....

[@loganreidy7055]

Anyone ending up here 10 years later before finals?

[@Dann.heitor]

Man, i have a really important question: Who was calling? Hahaha just kidding, thanks for the class!

[@niranjanwagh5767]

why integration of zero is zero? If taking derivative of constant is zero. Then taking integration of zero should give us constant. Right? What am I missing?

[@Bangalidude]

Legends serve millions of souls with knowledge 🎩💙

[@htercas]

nice job, man. But just a remark (it will not change the result): actually, the Laplace transform of a derivative is "-s" times de Laplace transform (using your notation). But that is very nice! CHeers from Portugal.

[@DGCAD]

Great!!! You are a master!!! But one question: What about if you don't have initial conditions? For example if you have this equation y^(IV)+13y''+36y=0 and you haven't the initial conditions? How resolve it?, Do you have some video explanatory of this case? Thank you very much Excellent video.

[@liquidstl]

@Jarrkha I am an engineering major, and am not required to take linear algebra. I am going to anyway since its one of only 2 more math classes I need for a minor in math.

[@pedrogacek800]

Thank you so much

[@weneedabeats9750]

this video help me a lot

[@medwatt]

Why is mathematics for engineers always made so easy !!!

[@danielwoodford]

Been watching your vids, so much easier to understand, making it seem so easy. Do you have any examples realting to R.L.C electrical circuits? Thanyou

[@gremlinextreme101]

i'm getting this after 6 months of calculus, so just read around a bit, it isn't too bad

[@waltermt22]

Thank you very much for this!!! You are doing a great work!

[@oneandonlyjark]

@liquidstl Ah, you see? 'tis unavoidable. Linear Algebra is sooooo useful -- and its actually kinda fun to do, since there are so many equivalent theorems.

[@okabc]

i know its a tab, but even if its a mouse i spent a while practcing and didnt take long to get average hand wrtiting. now if i did that many vid i would have awesome mouse writing ability :D

[@jimlov04]

Hi, AWESOME vids! Can u make some videos explaining fourier transforms and z-transforms?

[@esraugur485]

Which program are you using as a blacbrad? Thanks.

[@asif7240]

Thanks

[@oneandonlyjark]

@liquidstl It depends on the engineering, obviously, but a lot of the more math-heavy ones that are "popular" here in Canada invariably teach it in some form or another. I think efficient program maps give you the perfect balance between prerequisite math courses and actual engineering courses, so that they dont waste time teaching you math in the courses that matter, but dont waste your money and course load with courses that don't matter. ;) This vid poster has a nice speaking voice.

[@GroznyjGradHunter]

I love you man, life saver

[@ehoss07]

Thank you!!!!!!!!!!!!!!

[@obogz]

You rock!!!! Thanks alot!

[@jngggggggg]

very nice! and you write very well using a mouse

[@Frostbitecgi]

maki videos over quantum physics and tensor calculus

[@emdadulhaquemilon9484]

Thanks a lot

[@gino6680]

how do you turn this subtitle thing off?

[@skateboarder501]

is this Mr. Thomas from the K12 Curriculum as well? The voice sounds the same

[@binxxx1992]

thank u sooo much

[@JiaJiaIsHereLa]

What if the question state y=5 instead of y(0)=0? Need help.

[@CopyableRug]

You're a champ.

[@timvw01]

great video

[@MrPineapple921]

how can i learn these ? I wanna learn these rulls

[@willyou2199]

5:20 There's a sL{f'(s)} and 5L{f'(s)}. I was pretty annoyed why you didn't just directly substitute L{f'(s)} in the above line, and then i saw you could factor the (s+5) together, and i'm like hey this guy is smart. I regret that thought.

[@mayasinsight9911]

Good explanation but for everyone there's a slight mistake in formula .. kindly reconfirm

[@DhavalSakaria]

niceeeeeeeeee

[@wilso347]

12 professors can't teach Diff. Eq. as well

[@bahrom7893]

@jngggggggg I don't think he is using a mouse. Probably using a digital pen.

[@Elzelgator]

God of Math..God of Math blessed us.. O.o

[@k28]

@jngggggggg he doesn't use a mouse silly lol it's a tablet

[@tobysmith5941]

I love you Sal

[@curtpiazza1688]

😊

[@steveju87]

he is writing with a penmouse...so that answers all that

[@alexanderjack5937]

You got a wrong answer at 7:50

[@xabcx]

you kind of sound like barrack obama! :] but anywho, amazing video! thank you so much!

[@emad.q.mohammad8145]

I want the solve of this differential equation using laplace transform Y'' - 3Y' +2Y = e^3t , Y(0)=1,Y'(0)=0 . I want the solution as soon as possible please. Tomorrow is the best please

[@sammy5576]

240 p *sad youtube noises

[@happyfunify]

cos i don't have space to write a curly L ...lol

[@suuuuuper123]

u seriously save my ass all quarter bro thanks

[@beneeravishta6224]

how do you get Y(0)=2 and Y'(0)=3 ??

[@mansuryesilbursa7553]

They are given to solve equation

[@coldwater5814]

god bless

[@pboeye]

nahh im not in algebra XD im to stupid for it XD

[@Zeletta]

@jngggggggg I think he uses a pen tablet

[@k28]

@GKrizzel lool

[@arpez]

no one going to comment on the equjation in the thumbnail?

[@omarmahmoud530]

can you solve this for me pls y'''+5y''+7y'+3y=2 given that y'(0)=y(0)=1

[@lorenz0laplace]

@jngggggggg lol

[@1807Danny]

too slow!!

[@abdulrahmanalsaffar1841]

thank but try to get to the point you talk a lot Anyway thank you

[@dopier12]

Can a foundation be set up where we can just pay to have this guy do only this and then we can just go ahead and get our degrees they're paying some worthless professors to get students frustrated in colleges and/or universities? I mean, how many people have to say they've learned things in 10+ minutes that they spent countless hours in class for while not understanding a thing? I don't mean to disrespect people who may have spent much money to get their teaching credentials, but I believe the students should have a say in how they're being taught. We all know that's not the case for some community colleges and public universities. I am attending a university in Miami, and I haven't been able to understand one professor. The ones who seem to care about students you can't fully understand. It's a nightmare! Our public universities need revamping!!!!!!

[@jamma246]

In a university you'd usually be expected to go way further than this. A lecturer isn't there to baby feed you; so far these videos have done extremely basic things that a student should be able to just read about on their own to be honest.

[@rizoph4371]

@@jamma246 Disagree. The course should teach me the fundamentals of the material because the expectation is that students are learning this for the first time. Reading the textbooks is usually only enough to get the general idea, especially with the absolutely awful textbooks my math department makes us use. Lectures should be there to clarify these concepts first, and then they can add complexity. I don't think teaching at a beginner level to beginners should be considered babying. That is like asking a 4 year old t-baller to hit a pitch. In theory, they should have the skills. They know the swing form and how to make contact, but they still need coaching to get those fundamentals before they can take the next step.

[@jamma246]

@@rizoph4371 I know what you're saying, but a lot of these videos are doing what the textbooks do in early sections simply in a more "visual" and slower paced form. So a patient student should easily be able to read through it and understand it, leaving more valuable time to talk through the more difficult parts. Honestly, the definition of the Laplace transform itself is pretty self-explanatory, as are the standard computations for basic function like exponential and trigonometric functions. If you don't follow those then it's nothing to do with not understanding the Laplace transform, that's an issue with grasping simple calculus that the student should probably go back and focus on. Surely what's more important is talking through the intuition and relevance, especially in how it's applied in more advanced settings, and some of the more complicated properties. If I attended a university where they spent ages just covering the basics I could read up in a book, I'd want my money back.

[@rizoph4371]

@@jamma246 Sure, some students can learn the basics on their own. But that is not everyone, and in particular not me. I am watching this video because my professor actually does not lecture at all this quarter (no joke, our classes are basically study halls and she sits on her iPad). Technically, the concepts are not hard. Technically, I should be able to use the textbook for everything. But I am here because I need human affirmation that my understanding is there. I am not asking for my professors to spend a whole 50 minute class lecturing the first level concepts (although that would be better than the zero lecture I am getting now). But if classes could spend even 10 minutes at the beginning level, students like me (of which I know many) would be able to get through class easier. It is great that you can get through the basics on your own. Frankly, I am jealous. But there has to be some fairness to students who just do not learn as well through textbooks. I do not lack in my fundamentals, nor am I lazy when it comes to studying. I have 4.0'd the freshman calc series. It is just that I have never done this before and human beings reach me more than walls of text. In short, people learn differently and if I am paying tens of thousands of dollars for my education, I would like that education to accommodate me at least a little.

[@jamma246]

@@rizoph4371 That's fair enough, and it sounds like your lecturers should be doing more at this difficult time. Out of interest, which part exactly did you find difficult about the Laplace transform, or were unsure of?

[@eduardedwin]

I like the way you said about your writing space as 'real estate'. Hahaha... Great video. Wish I found your video sooner. My Diff. Eqn lecturer was crap.

[@chrisfromca]

I like the way you said about your writing space as 'real estate'. Hahaha... Great video. Wish I found your video sooner. My Diff. Eqn lecturer was crap.

[@زوابعمختارة]

thank you very much for the clarification

[@nickbreezydotcom]

I really hope you're getting some form of payment from all of the work you've done.

[@gaenaegga]

u sound like tyrion lannister, thanks for helping me wit my assignment btw :D

[@pboeye]

i cant understand a THING XD but im only 15 years old so i think its normal XD

[@liquidstl]

@Jarrkha actually I did just figure out that I will have some linear algebra exposure in a class called engineering math, which reviews Differential equations, Calc3, and Linear Algebra/

[@oneandonlyjark]

not all universities. In fact some will teach Diff Eq concurrently with Linear Algebra, and some will only give engineers and physicists a one-semester course in lower-year Linear Algebra (i.e. "half" Linear Algebra).

[@harry8175ritchie]

it actually annoyed me thinking he was using a mouse, like, don't you feel uncomfortable writing with a mouse! I always knew it was a pen device but i don't know i think im just the definition of autism

[@DroneFragger]

This helped more than a year of maths lectures. Although thats because the lecturer we have had just lost tenure and quote "just doesn't give a shit anymore"

[@lequan6314]

love u man

[@Zpik3]

@jngggggggg A bit late, but I think he's using a writing tablet, like a wacom or similar.

[@phucle475]

You make it feel like real estate is a slow colliding place not where students actually get to learn real mathematics. Oh wait did i just raise my voice again

[@theyvegonetoplaid]

@Jarrkha you and I disagree completely on what is fun in life. just kidding ;)

[@gnes04]

i love u

[@cypherdras]

Why am I giving £9000 a year to my university for tuition when I should be giving it to this guy!? Thank you for helping me understand my course work. You sir, are truly a saviour. :D

[@juanchov182]

Thanks

[@CrazySmartx]

really i never saw that good explanation thank you so much. btw the solution is final solution right?

[@techgamer1333]

why we r doing laplace equation solving any suggestion?

[@calvinhobbesliker2]

how do you solve the equation if the initial conditions are not at y(0) and y'(0)?

[@habituallinestepper_]

@0asdf0asdf LOL These video's are great, and you sound JUST like Vince Vaughn!!!

[@tonytsai80]

@jngggggggg Its actually a tablet =]! He's a great teacher with VERY GOOD explanations!

[@atolzbro5727]

Some kind of marketing phone call😁😀😀

[@DelphianSociety]

It all comes together beautifully now.. this stuff is insanely easy

[@SammiScoop_1]

Thank you so much. I wish you were my professor.

[@AbinamiLivingJamala]

*tsk tsk tsk* too much porn *tsk tsk tsk*

[@alreadytakenindeed]

Thanks for explanation, very apresciated.

[@hdotkiddle]

You have saved many a degree pal

[@colombianamanrique]

thank you so much!!! god bless you

[@abrahamprashathapt4140]

Thank you sir.

[@Zappyguy111]

Thank you very, very much! I'm the only person doing math2010 and I was screwed up until I saw this video.

[@saint-vincentuzonwanne8296]

Hows life treating you now bro