Repeated roots of the characteristic equation | Second order differential equations | Khan Academy

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What happens when the characteristic equation only has 1 repeated root?
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Differential Equations on Khan Academy: Differential equations, separable equations, exact equations, integrating factors, homogeneous equations.
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[@gdullard]

i dont go to my DE class anymore and i watch these vids instead and i am one of the highest marks. I learned my whole class from this 6 hour playlist where everyone else learned it in 3 months lol

[@dipzahan754]

You are one of the greatest liars

[@m_wangu6572]

Imroz Zahan 😂😂😂

[@abhirajarora7631]

Like Imroz, I am not going to believe this.

[@urnoob5528]

@@abhirajarora7631 im

[@atitarndechasuravanit1227]

That skill of explanation is incredible, I love it so much.

[@cynthmae]

i just want you say again that you are super helpful. so thank you very much for making these videos!!!

[@fermixx]

dude you managed to upload 12 mins !
you should not worry about "ops, i running out of time" again.
thats good news

[@psychojoshie]

Could someone explain why when we look for a solution for a repeated root, we can find it by multiplying e^(-2x) [[[in the equation, y = ce^-2x)]]] with a function (in this video, v(x)?

[@bluppbullsson7508]

Thank you SAL!

[@grovestreet9165]

Genius

[@aniltk4919]

When you are putting the v' at 8:11 , its -4 but i think you are taking it as +4 and that way its simplified to v''. It should end up as (v''-8v'+8v). Am i not understanding a part ?

[@rajsk-jk9rb]

No bro he's substituting g(x) in very first differential equation assuming that g(x) a solution for y

[@einnor8006]

来了来了继续学diff eq

[@bleughbloop8569]

ill call this "ghee"...
continuing with the dairy theme huh?

[@BPMorais1]

(3 years after) did youtube use to have a 10 minute limit or something?

[@Rahul-mf2we]

Really?

[@mattaereal]

If the video isn't playing, just press L and then go back to the beginning if you want. Or skip to the very first seconds.

[@JDJosephDo]

Sal you truly are quite the human being. You've helped me for over 3 quarters of math now (from calc up to DE). You dedicate so much of your time helping everyone out you are helping improve the world (corny I know but true). Thanks man and I hope you continue to be successful.

[@diemilio]

I can't get this video to play

[@mertyigit4093]

If there is a heaven, you should be there man..

[@nanik373]

Most underrated channel ❤

[@MikeMesteller]

You're the reason I'm passing Dif. Eq.! Words cannot describe how thankful I am that you upload these videos!

[@Iamatheist1234]

I swear I will find the one person who voted dislike n erase him/her from the math society.

[@calvinhobbesliker2]

What happens if you use the method used here to find a second solution is used to find another solution to an equation with 2 distinct roots?

[@abdullah57habib]

I love you Sal.

[@shep9194]

mind exploded at the end there

[@alakbakbak]

It's confusing when you go through how to solve the problem the wrong way

[@DhavalSakaria]

yea

[@MrMark1431]

godbless you man... godbless you....

[@albert275]

holy shit. it comes together so well!

[@juliarawlinson7425]

Once again, thank you Khan Academy for teaching me what my professors couldn't

[@TheBaluchiterium]

They could, if they wanted. But professors are typically researchers, so they invest their time into that and less time into teaching. So it is expected that you figure out such things by yourself, by using books or with the help of Khan Academy.

[@swatmedown]

you are perfect , thanks very much !

[@othmandont9355]

Thank you

[@naomigathoni1563]

Poor handwriting

[@dobraOsoba]

awesome! :D

[@DarshanParajuli]

really helpful playlist, thanks mucho :)

[@ghalibhassan7047]

Thank you so much sir. It helped a great deal.

[@Alexa-xg2cv]

I don't understand how you solved v''(x)=0

[@mjtsquared]

To find v when given that v’’=0, just integrate twice. Integral of zero with respect to x is a constant, and the integral of a constant is just itself times x plus another constant. Don’t forget your “+C” when integrating

[@Motorol3k]

And how it can be solved if y''-4y'+4y = (1+x)e^2x?

[@fabianrestrepo82]

I believe there is a mistake when you are getting the 2nd derivative of "g"(6' 36"). I believe you forgot to finish the product rule and multiply by the first function v(x). so, correct term would be 4v^2e^(-2x)

[@urnoob5528]

no

[@hothotricky]

You were NOT concise on this problem. But I still appreciate your work and you did help a lot :)

[@adnanmustafa73]

The video is not playing.

[@luizmarangoni6024]

I had the same problem with chrome and could watch the video with IE. Try it out.

[@GenericPurpleTurtle]

Yes they did for a long time, it was under 10 minutes or it could be longer if it was under a certain file size (but a file size that roughly corresponded to 10 minutes) then they changed it so that if you were a youtube partner or director or something it could be longer.

[@neilrayno5437]

well then you have to find four, but what if one of them is chuck norris and the other 3 are his clones?