Power Series Solution for a differential equation

This differential equation will cover how to y'+2xy=0 with power series.
Check out my differential equation playlists for more lessons and tutorials: www.youtube.co...
4 popular ways to factor trinomial: • 4 popular ways to fact...
🍎 Support me on patron / blackpenredpen
#differentialequation #math #blackpenredpen

[@csegura26]

The first second of this video is really remarkable

[@damian.gamlath]

definitely cool. I love your way of teaching because you address the little doubts along the way, and explain why we are doing something, and why it makes sense to even think about doing it in the first place.. Something that alot of other youtubers don't do as well as you do. Thank-you :)

[@blackpenredpen]

27kdon I am glad to hear that! Thank you.

[@ameerzain6857]

you all probably dont care at all but does someone know of a trick to log back into an Instagram account..? I was dumb forgot the password. I love any tricks you can give me!

[@btiabdes]

222222222222222222222222222222222222222222222222222222

[@HolyHubcap]

Did anyone else notice his awesome 1 handed marker switching skills? Great video, very helpful !

[@Acoustic_Mutale]

2024 Engineers where you at?

[@hariszahid1311]

At your home

[@aiham_awd]

Here studying for my final exam in an hour

[@Arycke]

I have a degree in mathematics and I would have to say that it is always good that two methods yield the same answer for a problem 👍the power series derivation I'm sure will help those seeking to understand how to find a power series solution to a differential equation :D plus power series are so important in analysis so this is a good introduction to that as well. Great video!

[@JoQeZzZ]

How have you never studied power series solutions to n-th order differential equations while getting your math degree?

[@skateboarderlucc]

you misread...he said the video would be a good starting point for beginners (obviously not referencing himself).

[@abda7184]

Thank you very much for this informative explanation 👌👌👌👍

[@m.abdullah4518]

Bro your teaching method is goooood. Got my semester final today and this cleared power series for me which I wasn't able to understand the whole dam semester

[@SuperDreamliner787]

I´m currently attending a differential equations class and I have to solve one with the powers series method. Thank you for putting this up! Greetings from Germany! :)

[@seanfraser3125]

I think its great that you can find the solution in two very different ways. Yes, obviously the power series analysis is much more involved, but it also shows you another way of finding the general solution to the ODE. One of my favorite things about math is that there is almost always more than one way to approach a problem and find the same solution. Of course, if the problem on an exam was to find the power series solution to the ODE, I would just find the exact solution and find its power series. Saves a few minutes :)

[@blackpenredpen]

Yea, I like it whenever we can solve a problem with multiple ways. This could also be done with integrating factor as well.

[@jammcrusader1981]

dude honestly you are the man - i bought a shirt cause of how much you helped me

[@blackpenredpen]

Thanks! Greatly appreciated!

[@randys2669]

Recently got back into studying math, this is such a beautiful method for differential equations

[@blackpenredpen]

Hi!

[@indrada-rf2vu]

blackpenredpen hi :)

[@batubulgur]

blackpenredpen I just gave my math101 final and it went pretty well. Just learned Taylor and stuff like that. And seeing its usage to solve diff eq's is pretty cool. Love maths, still a lot to learn. I have a question, don't you have to calculate the remainder and show that it approaches zero? I mean, it looks just like e^x that gives us confidence but still...?

[@jordancastaneda7027]

"It's just like excel!" yes, yes it is indeed, thank you so much for helping me see it this way ! This is the easiest explanation I have came across so far.

[@alienmoondudes8071]

I laughed when seeing that xD

[@lalitverma5818]

Hi

[@ryujinryuk]

19:40 when u activate the asian mode........

[@marouanechokri3970]

LOL

[@tomatrix7525]

But he is Taiwanese

[@Hyperdrive]

@@tomatrix7525 Yeah Taiwan isn’t in Asia

[@tomatrix7525]

@@Hyperdrive I just got a notifcation with ur reply. I have no recollection commenting that so Idk what I was thinking. Of course it is jn Asia

[@josemaringarcia3335]

Thanks for making the re-definition of powers so easy to follow.

[@shayanmoosavi9139]

The power series solution is starting to click for me. Thank you very much :) P.S : 10:26 e cosine, e cosine, e cosine😁😁

[@Collinator02]

this guy is single handedly teaching me diff eq. ive had 3 teachers so far. 1st dude i withdrew from, graded ridiculously hard. made up stuff that only he understood. talked in an accent and wouldn't help. 2nd and 3rd taught the class together split in the middle. 2nd guy was alright just ranted about random stories sometimes. 3rd guy. sheesh. tiny asian dude who whispers. cant understand a thing he says, and when he does talk about something really important he just starts talking 20 times faster WHILE STILL WHISPERING. love you blackpenredpen

[@jennieferadombire926]

Thanks so much. I really enjoy your way of teaching, it makes the math so easy

[@Skull2121]

I needed this 4 days ago for my differenials final :,( i was searching all over youtube for a great video like yours! Keep it up!

[@Prxwler]

Woah, I haven't finished my calc 1 course and I find the first method overwhelming. Seems cool to be able to understand it AND replicate it, but knowing the second method exists made me feel a little relieved lol

[@EngSeifHabashy]

Man I love how you save me!!❤❤ I'm having my ODEs final exam after 2 days and I forgot all the methods and watching your videos right now

[@AkshatSingh-jf7uk]

You really helped me out i was stuck with this question for the past 5 or 6 minutes.....thank you

[@JacobKennedyowuor]

Wonderful. This has made sense to me for the first time. Thank you @blackpenredpen. I am writing an exam on Monday for Planetary Physics. Power series has been a nightmare. Not any more.

[@gaming_boga]

Sir finally found a maths teacher in my life plz keep uploading videos thnks!!

[@ВладКузь-з7ч]

if only I saw this 3 weeks ago...

[@Abdu_401]

I can feel the sad energy behind this comment ...

[@KadeW10]

Thank you so much! I was never any good with series solutions and this video helped me significantly! Thank you

[@user-yv8ue6rq5z]

The you explain everything is so amazing ❤❤❤❤

[@syaoransakura8839]

Wow, thank you. Your explanation save my TASK

[@hidude1130]

Dude you're by far the most talented bloke i've seen in youtube

[@deligentchacha5420]

this guy is a genius. Its an automatic distinction if you practice with Blackpenredpen

[@maryam_ahli]

THANK YOU SO MUCH!!! literally this saved my life!!

[@BernhardMetz-u1f]

Man, this one I can do exactly in my head and not need a series solution 😮

[@gamingwolf3385]

thank you a lot you are a great teacher , i love your style , and i start watching your videos instead of being present in my teacher boring classes hhh , i am kidding only , thank you a lot

[@ahmadalrjoub7352]

thank you, Very clear and easy explanation

[@wagsman9999]

Love your videos. Very clear. Help me with my calculus tutoring. Thanks.

[@thobilesikakane6113]

You are the best at explaining the harder stuff. I wish you could do pdes, i guess its a bit late for me though.

[@usmanjaved2350]

Outstanding dear.... I cleared my every point... Love you dear ♥️♥️

[@aylin_spg]

Thank you so much!!! You really help me I could understand it so well 👍

[@hassanalihusseini1717]

A nice week to solve it with a power series, as power serieses are very important to make calculations easier. Of course it would be much faster to solve this problem by separation of variables: y' + 2xy = 0 y/y' = -2x lny = -x^2 + c1 y=ce^-x^2 (with c := e^c1) I like your videos a lot, because they make me understand calculus deeper. Are you considering to make other videos on other subjects in mathematics, too?

[@Play-cn1ck]

Thank you for your detail explanation.

[@albajasadur2694]

Sir, you showed in another video lecture that a Laplace transform is in fact a continuous analogue of Power series. By using this example, can you demonstrate and explain why it is more handy to solve this ODE by using Laplace transform ?

[@gregorio8827]

Doing this integrating (using dy/dx notation) is extremly easy

[@davidhart1322]

Test in 5 hours. Thanks man.

[@abdulrahmanalaqeel1720]

the old way is about 1 million times better than this journey, thanks for the video very helpful.

[@inothernews]

Great video! I have not done power series solutions in a long while so this is a good refresher! May I know what your academic background is?

[@FrankMarquez-cc2ye]

Thanks dude!!

[@meedumdarshana1591]

Thank You So Much

[@amin2468]

Thanks alot, helpful as always.

[@blackpenredpen]

You are welcome!!!

[@raphaelseitz805]

thanks a lot for your videos blackpenredpen :) the only point i did not get was why a1 has to be 0. couldn't it be anything?

[@JerezMario]

I also found it weird that we assumed a1 was 0

[@souravchakraborty6766]

It's zero bc the right hand side is 0. That is why he set everything to zero. I hope this helps ;)

[@ostdog9385]

Awesome I love it

[@blackpenredpen]

Thank you!

[@sjoerdwiesmeijer7231]

That was really fun and insightful!

[@ennjoseph7311]

You are really remarkable ,, if only we could meet ,,you've been of so much help

[@hatsinze]

Thanks for the explanation

[@hichamitani6433]

excellent explanation: keep it up prof

[@emmanueladdo1430]

this video helped me in my math exam...thanks alot

[@JoanneCheptoo]

Bless your heart.

[@codedragon6237]

Great videos! Keep it up!

[@axlortega2881]

why is a1 equal to zero at 6:33

[@jayt675]

Awesome teacher!

[@araf-b]

Just awesome 🥰❤️

[@willilow]

eres un crack amigo,, gracias ,, saludos desde Chile

[@zavionw.8052]

Me: *looks at thumbnail* Also me: "whitetextredtext"

[@masterenglish7838]

awsome i love your way of teaching...thank you

[@blackpenredpen]

Master English you're welcome!!

[@masterenglish7838]

sir plz solve this y''-2xy=0

[@FuhrerShattercore]

Will you be able to teach us the method of Frobenius? It just appeared in my Mid-term exam and I've concluded that my professor is a sadist... and that it will appear again the finals. Thanks for the video anyways. :D

[@nischaldhungana7014]

did you get it in the finals?

[@mokouf3]

It is the Normal distribution curve!

[@dahazz]

Hey! Can you do an IVP and finding the singular points? THANKS!

[@amandabrandao3266]

this guy is a GOD

[@MirryKay]

Helpful

[@peerless3538]

Awww you are so cute.....🥺.......thanks for the precious help......Almighty bless you.....🙌🏻

[@user-se1hj5vx3k]

Very insightful

[@blackpenredpen]

Thanks

[@chritophergaafele8922]

I never see you solve a math problem that fast

[@MegaPruddy]

awesome 👏👏 👏

[@luckybruno5827]

Thank you so much, way better than my professor (:

[@Kurtlane]

Your videos are great, including this one. Just one correction; here you say several times "to compromise it." I'm not sure what is the right word here, maybe "to counterbalance it" or "to restore the original meaning," or something else, but it's definitely not "to compromise." It's not depressing, it's excellent!

[@blackpenredpen]

Kurtlane hi there! Thanks for the comment. My idea was like this: suppose u and I are making a deal, I give u two dollars, which means If i lose 2 then gain 2. Just like a trade. When I said this in my face to face class, my students understood it.

[@oqardZ]

Expression you are looking for is "to compensate for it".

[@blackpenredpen]

oqardZ that's for $ tho lol!

[@blackpenredpen]

oqardZ but I might also use that next time

[@davidgould9431]

English can be a wretchedly difficult language. I am a 56 year old native speaker with only a rudimentary grasp of any second language, so I am totally in awe of people who manage to be 98% fluent in English, so please don't take this as a criticism of the videos: they are all perfectly understandable but, while we are talking about English rather than maths, I may be able to cast some light. The problem here is that compromise has gradually taken on two different meanings, depending on how it's used exactly (grammar alert: transitive versus intransitive usage): "to compromise *something* " means to make that something worse or to create a bad effect: if you have a container of water and you make a hole in it, you compromise its water retention (because it will leak). If you say that someone has a bad temper, or is lazy or something bad, you compromise their ability to get a job: you make it work less well. You might say you compromise *them* in that case. "to reach a compromise" or just "to compromise" (but no object: " we disagreed, but we compromised."), which is what you are doing with your trading example, is to make a deal that is part way between the two parties' starting positions: if I want to sell you my car for $1000 and you want to buy it for $500 we might compromise on $750. Or if I want to go to the cinema and my wife doesn't want to see the film, we might compromise by going out for a meal: we both get an evening out, but not our ideal evenings. As long as we both enjoyed it, we reached a good compromise. To wheel out some gratuitous grammar, when "to compromise" is transitive (that is, it takes an object: you compromise *something*), you are making that thing worse. When "to compromise" is intransitive (no object: you just compromise with each other, say), you are reaching an agreement. As oqardZ says, in this case a native speaker would use "to compensate": you have made a change in one place and, therefore, you need to make a change in another place to compensate for that first change. Sorry: this is far too long a comment. As I said initially, the videos are great and easy to understand: it's just that , in this case, what you said doesn't mean what you think it means.

[@jay1435]

God bless you soldier

[@charlesrothauser1328]

I find the youtube commercials during this video a terrible distraction

[@kgotlelloramatsetse2162]

beyond cool!!!!!

[@xrisku]

I am watching this wondering why none of it looked quite familiar, until you did the old way. then a neural circuit instabtly lit up. :)

[@pratishamishra4142]

Thank u

[@jarikosonen4079]

a1=0 & series-sum=0, so it's all 0 then. But if series-sum=-a1, will it be all 0 then also? a1=5 & series-sum=-5, how would it work? Maybe nothing that need be proven.

[@calebe16]

Power series are interesting in some specific cases. I would like to know how to do with power series for non homogeneous differential equation.

[@w.a.domski]

watching this at 12am before my math test in 8am, and i haven't even studied power series yet (yes im an idiot), wish me luck

[@charliewilson3234]

Excellent stuff def not depressing.

[@PeterBarnes2]

Would it be possible to do a power series with the differential equation y' - ylnex + ay/x - by/(xlnex) = 0? I think that might be a pretty cool problem.

[@N8TheGr8M8]

Why do some people start the series at n=1 and some people start it at n=0 for the y' series?

[@iamprodigyable]

Im having trouble seeing how those two answers he found are equal to each other. I mean, I know they are, but i don't see it. can anyone explain?

[@saraaxx9100]

he has used the separation of variables method for the second time.. which's another method of solving differential equations

[@15jorada]

I'm a math major that is thinking about going to China to study abroad next summer. Do you work at a Chinese University? I would love to meet you. If not do you have any good recommendations for a Chinese University I could go to?

[@anatomania1126]

15jorada Dude he works at UC Berkeley

[@cencenpolinar3085]

for the second equation isn't n = -1 to make it x^n? thanks

[@zhylerliebesleid9771]

This is so interesting

[@yifengwang790]

what a god

[@john-athancrow4169]

I liked you finally said a .

[@jackkalver4644]

Didn’t even take me a minute! y=Ce^-x^2=Σ((-1)^n C x^(2n)/n!

[@drosos_strength_coaching]

Proper video title: why not to solve differential equations with power series even if your life depends on it

[@digbycrankshaft7572]

Nice

[@Juanksv09]

Jedi Marker Master

[@SomeOne-gh3tw]

i LOVE U

[@levi4328]

why couldn't we just set the summation to be equal to -a1? 7:00

[@hugocampos7894]

Perhaps a bit late but if I'm not mistaken it's because it's being multiplied by an X^n on the right and you can't really cancel that with anything inside the summation

[@hlamzar]

you're awesome

[@spectre3214]

0:00

[@kelvinadimas8851]

F A S C I N A T I N G

[@AdesanyaAyodejiCeg]

really good video. but my exams are objective questions.

[@lorenzolevy4708]

Can you hypothetically use series to solve any ODE?