ODE:: y'' - xy' + 2y=0 :: Power Series Solution about an Ordinary Point

[@zaferjesri4334]

Wow I was gonna scroll down to comment on how helpful this is expecting 1000s of comments, you deserve more views! This is the best explanation I could find and it's saving me for an exam soon. Thank you.

[@JonathanWaltersDrDub]

Thanks so much! That really means a lot to me! Glad I could help and I hope you do well on your exam!

[@allaboutlearning6467]

U r a lifesaver Nobody I have ever met has given such a good math solution Thank you❤

[@JonathanWaltersDrDub]

I’m glad to help!

[@kavehzamani816]

Explained the subject far more thoroughly and in a way where the concepts were much easier to grasp than my teacher had. I was so lost on this subject until I found this video. Thanks!

[@JonathanWaltersDrDub]

I'm so happy to have helped!

[@alexsasmrchannel]

Thank you for the clear explanation, it was really helpful!

[@JonathanWaltersDrDub]

I'm so glad it helped!

[@robertowilliams9217]

Clearest and best explanation on this topic, Thanks!

[@JonathanWaltersDrDub]

So glad this helped!

[@ElainaKyotoCat]

@@JonathanWaltersDrDub What happens if there is initial condition given? y(0)=1, y'(0)=2 Approximate the value of y(2) using power series solution. Approximate the value of y using only up to 8th degree term of the series. Write your answers in 4 decimal places.

[@Oscar-gx2yf]

Great video! You made this very clear for me thanks!

[@JonathanWaltersDrDub]

I’m happy this helped! Thanks for your feedback!

[@jacobalva7929]

Me: 'On verge of absolute breakdown' Jonathan: "Here is everything explained perfectly" Me: "Breakdown averted'

[@JonathanWaltersDrDub]

I’m happy to have helped! Thanks for your support!

[@automaticcaptions]

I have an exam in less than 6 hours... this is a life saver

[@JonathanWaltersDrDub]

Glad to help! Do well!

[@automaticcaptions]

@@JonathanWaltersDrDub thank you!🙏

[@rl_111]

13:15 - shouldnt we have (2ak) before the last sum?

[@christiannayre9931]

this tutorial saved my finals. Thank Senpai!

[@JonathanWaltersDrDub]

I’m glad this helped clear up your understanding!

[@mohamedtaha3574]

i have an exam tomorrow and you saved my life

[@JonathanWaltersDrDub]

I'm so glad this video helped. It served it purpose! Thanks for watching!

[@narendracharugundla2209]

if we want to find the solution of the differential equation y''-3xy'=0 with the help of the power series around x_0=1, then the reccurrence relation to obtained is?

[@AdunHerself]

Thank you for the detailed explanation

[@JonathanWaltersDrDub]

I’m glad to have helped!

[@ericelms7038]

At 15:00, does the answer have to be linearly independent? Or are we just assuming it is so that we can solve it?

[@JonathanWaltersDrDub]

At 15:00 we are using the fact that 1, x, x^2, x^3, x^4, ... etc... are linearly independent to set the coefficients = 0 so we can find the recurrence relation.

[@nathandyson3462]

at the end shouldn't the third term c_0x^2 not have been included since the series started at k=1 and not k=0?

[@HAYA3992-j5p]

amazing teaching skills !

[@JonathanWaltersDrDub]

Thanks for your support!

[@mayararamos5201]

Thank you soooooo much, this helped me a lot dude!

[@JonathanWaltersDrDub]

Awesome! I’m glad this helped!

[@komagama3907]

thanks to you I covered all of the DE 's you are great :D:D:D:D

[@JonathanWaltersDrDub]

Thanks for your kind words! I try my best! I’m so glad this helped!

[@hassanmaalim23]

Stay blessed, you really assisted me

[@JonathanWaltersDrDub]

I’m happy to hear that! Thanks for your support!

[@samuelbassey6806]

Thanks for sharing

[@Eric_Kamau_Wambui]

Question please: Why do we have K greater or equal than one in the recurrence relation? Check on the 16th to 17th minute

[@JonathanWaltersDrDub]

Sorry that I missed this! k is greater or equal to 1 because the series terms start at k=1. Since the recurrence is from the terms inside the series it's only valid for the k values for which the series is defined.

[@nedh8493]

this was super helpful, thanks a lot!

[@JonathanWaltersDrDub]

Thanks for your feedback and your support!

[@natnaelberhanu-i8w]

Can we reindex but have the same variable we had originally. For example, could we still use n as long as we are reindexing instead of k?

[@JonathanWaltersDrDub]

That is okay but you just have to be very careful. It would be like doing a u-substitution in an integral but still just using x.

[@twesigyebob8385]

Very well explained keep it up

[@JonathanWaltersDrDub]

Thanks for your support!

[@margaretonu223]

Simplified and helpful💗

[@JonathanWaltersDrDub]

I'm glad this helped!

[@TanJunYu]

thank you so much!

[@suhailawm]

Thanks aLot Sir. Very usefull. Love alot sr

[@JonathanWaltersDrDub]

Thank you for your support! I’m happy this helped!

[@khaboignatia4662]

Simple and clear.....thank you

[@JonathanWaltersDrDub]

I so happy to have helped!

[@raccoon3440]

you are the GOAT

[@JonathanWaltersDrDub]

🤣 I appreciate your support!

[@myuyenang1372]

thank you so much

[@JonathanWaltersDrDub]

You’re welcome!

[@sadee9396]

Thank u very much sir.

[@JonathanWaltersDrDub]

You're very welcome! Thanks for your support!

[@charinduthisara3017]

thanks a lot

[@JonathanWaltersDrDub]

You are welcome! Glad to help!

[@ALVARADO121]

imagina no enterder nada en lo absoluto de estas series y de remate no entiendes ingles :( jajajaja gracias me ayudara para mi clase(espero)

[@JonathanWaltersDrDub]

¡Me imagino que es muy difícil! ¡Mantener el trabajo duro!

[@kkrrho_py]

My exam is in 1hr. Lifesaver

[@redzone7787]

simply??? hm.... (thx for the awesome video)

[@JonathanWaltersDrDub]

Thanks for your support!

[@muratcanakdogan26]

Do you do the solution in this process? y''+xy'-3y=4,2x y(0)=0 y(1)=1,9 Δt=0,25 dissolve on paper please at least

[@DanielTamayo-y3f]

so how is 2*3 equal to 3! ??

[@batuhanbozkurt7838]

Hello! 𝒚′′ + 𝒙^2𝒚′ + 𝒙𝒚 = 𝟎 y(0)=0, 𝑦′(0) = 1 Solve the differential equation with the power series. Can you solve this question?

[@giovannicabrera8808]

did you solve it?

[@dianasofiaramirezvillamil6486]

Hold on what happened to the X he forgot the X

[@JonathanWaltersDrDub]

I think I almost threw up when I saw your comment. I got a little panicked to say the least ! 😅. Maybe check 5:18?

[@davidbanda2124]

Which x

[@ReachYourGoalsYT]

Thank you. You made me understand power series

[@JonathanWaltersDrDub]

I’m happy to hear it’s clicking for you now!