Boundary value problem, second-order homogeneous differential equation, distinct real roots

[@naimmuas]

OMG! I know every teacher has their own teaching style but the way you teach just.. wow. You are great!!

[@bahaatamer1245]

I have lost count in how many times this amazing tutor has saved me from dead-confusing slides! Thank you Krista (for the 1000th time! :) ).

[@kristakingmath]

Awww thanks! I'm so glad the videos are helping!! :D

[@bahaatamer1245]

@@kristakingmath they definitely are - when the slides make no sense, it's Krista! 😀

[@dingviet4310]

Hi Krista, I just need to tell you that I would *not* be surviving my second year of calculus if it weren't for your skill and generosity in creating these videos. You are a real force for good in this crazy world. Please know that I am so, so, super grateful that you exist - and I genuinely hope that good things happen to you in your life. :')

[@kristakingmath]

I'm so glad the videos are helping you along the way! Thanks for the support. :)

[@crusiethmaximuss]

I am not sure why this was recommended to me by KZbin, but you kept my interest throughout your whole lecture. Thanks 🙏 for the video.

[@cameronmcmillan9288]

So easy to follow. Been searching everywhere for an explanation like this! Perfect, thank you!

[@kristakingmath]

Thanks for the feedback! I'm glad it could help. :)

[@Univeristy1]

Thanks, your efforts make it easier to deal with ODE

[@AJCook-on1in]

You make this so easy to understand, thank you!

[@kristakingmath]

You're welcome, A.J., I'm so glad it helped! :)

[@SatyamSharma-is5rh]

Such a beautiful n sooting voice.... Makes rest easy. ...💛💛

[@SW-2010]

Excellent video. Thank you

[@stevenson720]

thank you. very comprehensive.

[@dominic9631]

This was extremely helpful. Thank you so much!

[@kristakingmath]

Awesome! Glad I could help. :)

[@WateryIce54321]

Thank you, that was a clear explanation. Though, I have to admit - I am fairly slow at math, but I feel like this explanation took longer than necessary for such a simple problem. Nonetheless, thank you for your helpful efforts!

[@kristakingmath]

WateryIce54321 You're welcome!

[@SoloPro]

great vid and hope you always keep doing some more... since I was struggling to understand my lecture notes I decided to try my luck on youtube and then you popped out... I wasnt sure if it would be good but It certainly was :D

[@kristakingmath]

+SoloPro Thanks, I'm so glad you're liking the videos so far! :D

[@SoloPro]

CalculusExpert.com yh they are really good.. your students are lucky to have you as a teacher ..

[@zacharyahearn4069]

This was very simple and helpful.

[@Stunktank]

Phenomenal explanation. Thank you so much.

[@kristakingmath]

Thanks :)

[@guitargod10940]

How would you do this for a partial differential equation?

[@douglasstrother6584]

Separation of Variables transforms a PDE into a set of ODEs. mathworld.wolfram.com/SeparationofVariables.html

[@vdwest4592]

Keep up the good work uploading your videos. A colleague of mine is passing Differential Equations thanks to people like you!

[@kristakingmath]

Thanks! I'm honored! :D

[@Mathlog]

Hello ma'am your tutorial is really impressive. I want to know about your writing process;about the virtual black board.please let me know. Thank you

[@kristakingmath]

The blackboard program is called Sketchbook, and it's made by Autodesk. Hope that helps! :)

[@Mathlog]

@@kristakingmath thanks for the reply ma'am.

[@kjanling]

Initial conditions are used in initial value problems. In your case, a boundary value problem, so the conditions are called boundary conditions...

[@dinaoltadesse]

Just a friendly advice, please post the links to the videos of the things you touched on through your videos. It could exponentially increase your number of views and also help us better understand the subject. Other than that your a fantastic educator 👩‍🏫

[@andreamagnanini3196]

why you call y(1) an initial condition if you say y(0) to be one?

[@douglasstrother6584]

She should say "boundary conditions".

[@Dinho675]

Your channel...your videos helped rid me of Calculus II and III. Thanks a lot. ;-) (finally free of calculus...hahahaha)

[@kristakingmath]

LOL, congratulations! I'm so happy for you!! :D And I'm honored to have been able to help! :)

[@Tewfik]

what happens if ur initial condition is y''-y=0 (the y doesn't have a prime at all) is the value for y=1? (cause y''=r^2, y'=r) thanks for the great tutorial!

[@kristakingmath]

+kevthehero22 Yes, exactly. You can think about it as r^0, which is 1.

[@Netharino]

very very helpful thank you soooo much!!

[@kristakingmath]

Glad it could help! :)

[@Kazshmir]

That was a pretty vague definition of boundary vs initial value problems. You're saying the difference between the two is that sometimes we can't solve boundary value problems.

[@douglasstrother6584]

Boundary Value Problems users.math.msu.edu/users/gnagy/teaching/12-spring/mth235/L33-235-ss12.pdf

[@khuonghuynhquoc6184]

I thought you were supposed to use cramer's rule to find c1 and c2

[@douglasstrother6584]

Cramer's Rule is overkill for 2 equations w/2 unknowns. mathworld.wolfram.com/CramersRule.html

[@meserettesfa7208]

good job

[@enggguy]

Why is y converted to r??😢

[@danzai8762]

Just wow ♥️

[@thewhizkid3937]

What happens when the roots are equal?

[@saif8912]

awesome

[@aniruddhmodi6522]

How is it a boundary value problem if the conditions are of initial value

[@Mathlog]

In conditions x has two different values 0&1..that's why

[@douglasstrother6584]

She should say "boundary conditions".

[@audibenz5908]

Thank you so much....and hey ur voice is so sweet

[@jakeyaboi6824]

Amazing.

[@kristakingmath]

Thanks, Jake! :D

[@sumit803]

Wow mam yuhh r so good..love from india😘😘😘

[@mondair99]

You rock-eth. :D

[@LearnWithFardin]

💝

[@bimp1685]

please talk slowly :/