Laplace transform solves an equation 2 | Laplace transform | Differential Equations | Khan Academy

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Second part of using the Laplace Transform to solve a differential equation.
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Differential Equations on Khan Academy: Differential equations, separable equations, exact equations, integrating factors, homogeneous equations.
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[@alecrosema4885]

Sal explains so well i'm still watching his 240p videos from 2008, in 2020.

[@skaomega3487]

2022 here

[@HateNoobsGR]

@@skaomega3487 2023 lol

[@RocketsNRovers]

@@HateNoobsGR will watch in 2024 aswell

[@mumujibirb]

2023

[@nathanielajayi5827]

2023🎉

[@nathalie12890]

you've taught me laplace transforms in 30 minutes better than my college professor did in four 50-minute class periods. You are making higher education material into public domain! THANK YOU!

[@st3amyjimmy]

"something you probably haven't used since algebra 2..." I never learned partial fractions until calculus 2 my sophomore year of college

[@LordHav3Mercy111]

Right??!!

[@kylo_mylo1088]

10 bucks says when you learnt it the lecturer said "as you may remember from highschool...."

[@rishiksarkar9293]

This helped me a lot and my concept now is very clear....thanks a lot sir, u explain very nicely

[@GolddiggerCG]

Laplace has finally clicked, thank you!

[@anorman728]

I'm currently in a math modeling class, which involves ODEs. I haven't done ODEs in probably two years, and I wasn't any good at them then. I don't know if you ever see these comments, Mr. Khan (since there's so many of them), but I just wanted to say that I made a 98% on my first test, thanks to you. The stuff you're doing here is amazing, and a lot of us are very thankful.

[@DroneFragger]

Yeah this is actually taught much better than the way my professor taught it. He taught it like the laplace transform was some kind of magical dimension without actually explaining how to use it for anything practical or how to even turn stuff into the s-domain.

[@seppestas]

I had some terrible mistakes in my notations, which caused me to fail my exams the first time (even though Fourier came very natural to me...). Thanks to your videos on Laplace transforms and partial equations I found the stupid mistakes, and it all became clear. You change peoples lives all over the world, thanks a lot!

[@Redline582]

This partial fraction expansion allows for an easier method by cross multiplyings A/(s+2) and B/(s+3) and setting it equal to the numerator of the left side of the equality;this results in 2s+13=A(s+3) + B(s+2). Set s=-2 to solve for A and set s=-3 to solve for B.

[@kavoos1000]

GOD BLESS YOU , i mean so clear and easy you let it look like... you are simply one of the best , i think many people will adore you ...and you are already famous

[@dimasnazlibahaduri7104]

the 9:12 is a big oooo moment for me. Thank you sir,this helps me on final exam

[@cemcalsar7367]

same hahhhaha

[@GreenNutts]

Sameeee

[@hughlamont3696]

This is incredibly useful for solving vibrational responses.

[@gogodooy]

me salvaste la vida! me perdi esa clase en la universidad y ahora puedo ver como funciona la transformada de laplace! muchas gracias

[@uberloss]

University of KZbin is THE BEST!!

[@randomisrandom]

Cheers! Great refresher for the exam i have in 7 hours :)

[@surgicalstrike11]

Wow, I never took differential equations, but that technique is so cool! Your comment at the end intrigued a lot though, how do you go about proving that the inverse of the Laplace Transformation is one-to-one?

[@Helfi92]

With khanAcademy, my grade goes up to 90's if not higher. Without khanAcademy.. I will most probably struggle to pass

[@brambeer5591]

That enthausiasm when a beautifull solution is almost found, at 7:24 you say "let me just stay consistent".

[@aqil2211]

2021 & still helping souls out there

[@atown2k3]

thanks for the vid..i read this in my text book like 10times and didnt get it but your vid made me undestand the procedure of doing these questions...thanks.

[@eurosfinest1234]

wow this is what you call a lecture! thank you so much!!

[@MartinLarsson]

Brilliant! And I love the slow evolution of the number 13 into the letter B :) I'm almost thinking you throw these things in on purpose just for fun :)

[@vvvviktorrrrssss]

your videos really are usefull a lot, thanx about that, keep doing it!

[@thomasseillers3905]

Learning Engineering in 2021 and this is the best Video on it

[@OldRaven2529]

Thank you so much. Your vids are very useful.

[@josexlvi2]

thats how a class should be-- on internet

[@nefariouskarl3995]

Lmao, poor laplace got roasted two seconds into the video

[@waltermt22]

Muy util! Saludos desde Bolivi.a Very helpful!! greetings from Bolivia!

[@andyalice6673]

Thank you! This is excellent.....

[@nilatstc]

does the laplace transform work on ALL differential equations?

[@fidelnyengera1340]

Sir you are funny and friendly 😊... I understood everything thank you

[@hagenimanagilbert7860]

Thank you a lot sir! I have definitely satisfied with this amazing explanations. You deserve much respect by the way.

[@TheMarkoanton]

OMG this is brilliant !!!

[@mitchyd89]

Could you generally explain that method or send me a good link if you want? Does it involve mult the origional fraction by the denominator of the new partial? Thank you!

[@d3us89]

Dude, you are a life saver!!! :D

[@osoriano]

@supertren yes because (A+B) S + (3A+2B) = (2) S + (13) The terms in the parenthesis on each side must equal each other. Therefore, A+B = 2 and likewise, 3A+2B = 13 hope that helps

[@cucumberguy]

you made it look so easy. wonderful! =)

[@nathancommissariat3518]

Thanks Sal. You are the GOAT

[@krruger79]

@krruger79 BTW we compare polynoms.Both sides of the equation (A+B) S + (3A+2B) = (2) S + (13) are polynoms of variable s. Polynoms are equal if they have equal corresponding coefficients.

[@harry8175ritchie]

i agree completely but im wondering how you're doing university level calculus with english skills like that

[@GreenNutts]

I was so close to giving up the video. But my stubbornness of watching pt.1&2 kept me here hesitantly. Until the big omg realization happened at @9:00. Big help for the ECE majors ♥️

[@asif7240]

Thanks!

[@宝宝-n8q]

Thanks very much. Great guy!

[@peras3000]

I've learned a lot with your vids! =P I haven't found the non homogeneous equation video =S Thank you ;)

[@xabcx]

"hairy" haha his favorite adjective

[@abhimuscat]

Wow ! Does chemistry by any chance involve Laplace transforms?

[@MrGrim1993]

You sir, (imagine the best compliment you can think of and insert it here)

[@sammaltzman5908]

Ik the laplace transform is supposed to be more efficient than previous techniques taught in differential equation but I feel like this took way longer then how I would’ve solved it without knowing the Laplace transform lol

[@rezmo9818]

great video!

[@Sawer89]

really good video ty man

[@acer57]

extremely helpful !!!!!

[@xkamykkk]

thank you!

[@krruger79]

@supertren You are lost in details. We are looking for value of A and B not supposing its as you did. For what reason you let exemplary value of 3A+2B?

[@drewforyou]

4:21 "Notice: in all differential equations, the hairiest parts always the algebra." This man has forgotten about taking integrals involving trig identities i suppose

[@takemeway]

you are the best !!!!!!!!!!!!!!!!!!!

[@meetthakkar90]

my test is tomm and you saved my a** !!! thnx god

[@GuilherHast]

I said many times it was 13 he finally got it in 5:14.

[@mejdbaba]

You are so so good man.

[@studdmuffins1]

This guy is my hero

[@paderp1528]

ABSOLUTE FUCKING GOLD!

[@famguy218]

Wow; I love you so much.

[@ttian2]

@h0wud0in2 you are right, most times we should blame ourselves instead of the teacher. however, you cannot understand how hard it is for a student like coolsulemanboy or me, my friend. i tried my best working hard on math but i only got minimum pass for my every university math course. meanwhile, i got many A's and A+ on music, economics, finance, and statistics, spending only about 10% or 20% of time comparing to math. talent really means more than hard work, IMO.

[@panchalmihir3174]

Would anybody please reply my question? Question is " why we use exponent as in every method.i think I partially get thos because its a most the growth can any function have." Am i right please let me know.

[@urdouchbag]

awesome video....I do have a question at around 2:14...you used partial fraction method to solve that inverse laplace ...however there's this kickass theorem ''heaviside theorem' which makes such transformation easy(our math teacher taught it to us)..could that be used as well in that situation ...? love from India

[@PooleH]

Thanks mate

[@Lambitay]

its the same for convolution method :D

[@supertren]

@mypimpomar "The terms in the parenthesis on each side must equal each other. " Well...not necessarily.. For example if: (3A+2B) = 0; then (A+B) S = 2 S + 13

[@ABHISHEKBADIAL]

dude u rock man !!!

[@hewadewageashan9592]

Superb

[@bam906]

@thedevilrides very ironic that you misspelt mistakes

[@omrodez]

how would you solve something like this? L{Y}=[(s+2)/(s^2-s+6)]

[@LudwigvanBeethoven2]

Beautiful

[@niharikagarg9300]

Sir, can we solve this problem by completing the square in the denominator, but my ans is coming in the form of Sinh x and cosh x... Is this the wrong method????

[@Juliasn68]

The only videos where I can appreciate 240p

[@GreenNutts]

😂😂😂

[@supertren]

I dont understand why in this equation: (A+B) S + 3A + 2B = 2 S + 13 He says that A+B = 2 In the minute 5:00

[@TheReligiousAtheists]

But how can we be sure that we can't add something to a function (other than 0) that won't change it's Laplace transform?

[@jettubes1]

really Awesome video :)

[@Culerpica660]

man you are great :)

[@wackojackgoff]

Thank god your doing maths i wouldn't recommend doing anything involving proper english

[@shubhamojha1]

hey man i want 2 see all ua videos at a time plzzz can u send m d link 4 watchng all ua videos in an ordere plzzzz man....n ya thanks alot u jus awsum...:)

[@bethel1n]

good job :)

[@barrymarkakatah347]

Sir, how do I solve y' + 3y = 0

[@jibraniqbal9315]

@@blackturtle1841 you're correct, usually just put y(0) as C and u can solve the differential equation if u have y(x) for values other than x = 0 .

[@karla011302]

ahhh thank you

[@karla011302]

why did you multiply -2 to A+B=2, im a little confuse about that....HELP

[@harismasoud2173]

Its 2024 and I still watching your 240p video

[@pravinvedurla6787]

"We have all this hairy mess". I fell off my chair. Lmfao!

[@oshraideh]

thaaaaaaaaaaaaaaaaaanks a lot

[@TheAZAQ]

야이생키야 형이 격하게 사랑한다... 니덕분에 군대 2년 유학 1년 노가다 2년으로 다 까먹었던 라플라스 변환이 뭐였는지 다시 기억났다 촙내 고맙다 이생키 한국오면 연락해라 형이 밥사줄게 ㅠㅠ 흑 I'd like to link it to my web site :D thx my genius !!! I really forgot a f**king Laplace Transform coz I spend 2two f**king years for korea army. (it's duty if you are a KOREAN) .. anyway I remember that. from Ur youtube! thx :D

[@pavithrateiyagu9927]

can anyone exlain how he got A=9, i m confuse about why did he use -2A-2B= -4

[@GreenNutts]

He did to make A the solo variable

[@bgtops]

How do we know what set of factor to use because this function can also b broken into (s+6)(s-1) but the answers are different

[@frenchieewoo3355]

Percy Richmond that actually is not the same factorization. When you distribute that out you end up with . s^2+5s-6 which is why you get two different answers. I know I’m late just explaining for anyone else who may think this way.

[@rhall4th]

Is it just me or does this guy sound a lot like Ken Dashow on Q104.3 FM NY?

[@bethel1n]

good job :) your writing skillful using mouse, too

[@CodeDemystified]

Findt die Laplace Transform fur 6y^(2)+5y^(1)+4y=0

[@LordHav3Mercy111]

wie dunt zie findt ich thyself?

[@Incrue]

like that, i hate to guess solutions

[@hkhong]

Why 13 become B?initially it was 2S + 13,in the middle it became 2S + B?

[@toozydude2]

It was a mistake he made. Because the 13 looked like a B. He realizes this mistake in the video and changed the B back into 13.

[@katrinamaeacha7661]

Where did he get -2A -2B = -4 @5:43?? Somebody enlighten me

[@psychedelatorre3470]

He multiplied the whole equation (A+B=2) by -2 so that he can eliminate B to get the value of A... :D

[@psychedelatorre3470]

Hello Acha :D

[@katrinamaeacha7661]

Hiiii!!! Kasabot na okssss sykesss!! thank you sykesss!!! ;)

[@supertren]

@krruger79 Because I don´t understand it.

[@navidshahed4569]

good job...but dude why did you do that partial fraction expansion like that !?! go watch your own 1st video about it... XD

[@M_VERICK]

Not all heroes wear caps

[@bgtops]

The function can b factored two different ways (s+2)(s+3) or (s+6)(s-1). How do we know which one to use because you don’t get the same answer?