Linear Differential Equations (KristaKingMath)

[@calebv6410]

You just explained in 20 minutes what my professor couldn't do in 2 lectures. Thank you so much.

[@thearchitect27]

I hope you realize that your awesome teaching skills are helping the next several generations of engineering, science and technology students! Keep up the good work!

[@kristakingmath]

The people watching still have to put in the work, but I hope I can help along the way!

[@Randomname47689]

Just found your channel and I am so glad I did. My math professor does not teach me well, but you are clear when explaining and very helpful. Thank you for making these videos!

[@kristakingmath]

+packersx3x33 You're welcome, I'm so glad they're helping so far!

[@e9h9hoho]

My book goes off on all sorts of tangents and explains this over six A4 sides of tiny text. It's a relief to see a clear demonstration. Thank you.

[@priscillasue5228]

I really appreciate when you explain everything in detail. You've helped receive A's for calculus 1,2,3. Differentials seems to be going that route as well. Thank you so much for you making videos

[@kristakingmath]

+Priscilla Suarez I'm so glad I could help! You're obviously doing great with your math classes, so keep up the good work, and good luck with the rest of Differential Equations!

[@priscillasue5228]

XD You're AWESOME!!!!!!

[@kristakingmath]

You're welcome!! Glad you liked it! :)

[@kristakingmath]

I'm glad I could simplify it a bit! :)

[@metaphyzxx]

I love that you actually explained how the LHS is a result of the product rule, as well as how to recognize it. A whole semester in study, and you helped me get it in 10 minutes...

[@kristakingmath]

+Joe Richardson I'm so glad it helped!

[@kristakingmath]

You're welcome! Thanks for the comment. :)

[@MrDerekkk]

I've gone through 3 videos on this topic, this was the best one. Thanks! Btw, keep this format of presenting your solutions. Its clear and very easy to understand without a giant hand blocking the working.

[@Captain_Rhodes]

your videos are always clear. def one of the best teachers in all of youtube. thanks

[@kristakingmath]

Aw thanks!

[@kristakingmath]

Hi! I plan to make more of those types of videos. :) Although it may not be for a while.

[@PythonDelta]

OHH MAN, this really helped me after being stumped on one homework problem. Thanks a ton for the clarity of this vid!

[@kristakingmath]

Yay! Glad it could help!

[@collegeguy1325]

so I got a solid A in multi calc because of your videos and now ill be getting a solid A in my differential calculus too. Thank you Krista for making math fun and easy!

[@Mary-xs2jp]

Your explanations make differential equations look so easy. Thank you!!

[@dingviet4310]

Krista, I've commented like thrice over my 2 years at college already, and I just have to do it one more time. You are a pedagogical genius. Seriously, I hope you're a teacher/professor IRL.

[@kristakingmath]

😊

[@goosesicle]

I've been trying to figure out if Q(x) can have coefficients and you're the first person who mentions it and shows an example, im glad i watched your video :D

[@kristakingmath]

I'm so glad it helped!

[@kristakingmath]

Great question! :) They mean different things. The D_x tells you that you have the derivative of e^(3x)y. dx tells you that you're integrating with respect to x. In other words, when you take the integral with respect to x, of the derivative of e^(3x)y, you just get e^(3x)y. :)

[@thehobbyshop5154]

Great work ! simplified things to understand. May you prosperous!

[@kristakingmath]

Thank you, Amir! I'm so glad the video helped clarify things! :D

[@kristakingmath]

You're welcome!! :) So glad I could help. :)

[@kristakingmath]

Love you too! I will try to add more of these... I'm going back through all my calc 2 vids now and filling in gaps. Some people do some of this in calc 2, but a lot of people don't study it until Differential Equations. But it's totally understandable once you start learning it, right?! :)

[@AntonioMudge]

Every time i see your videos i feel that i fall more and more in love of math and You :)

[@akashraju8090]

Excellent video krista ! i really appriciate it .........refreshing video from the basics with proper steps

[@kristakingmath]

Thank you so much, I'm so glad you liked it!

[@Socrates271]

Wow, in the first five minutes you explained it more clearly than my calc teacher who would be teaching this for 2 hours and still no one understand it.

[@kristakingmath]

Thanks!

[@yichenyan8820]

This is soooooo clear and helpful, thank you Krista!

[@kristakingmath]

+Yichen Yan Yaay! Glad it could help!

[@kristakingmath]

you are so welcome! :)

[@kristakingmath]

awww you're very sweet, thanks! :) i haven't worked extensively with textbooks specifically for DEs, but James Stewart's Calculus, 6th or 7th edition is great for linear DEs, like the one I do in this video! :)

[@DanielFlanigan]

Thank you!.....I've looked at 3 different tutorials to solve 1st order linear ODEs, and this was the only one that helped!

[@VicktorPharrell]

Omg , you are freaking awesome, I literally didn't understand anything in all my ode classes, I love your videos so much 👌🏾

[@kristakingmath]

+VickTor Pharrell (ICE) Aw thanks! I'm so glad they're helping!

[@ruthanderson5717]

+CalculusExpert.com ; 0

[@kristakingmath]

I'm sorry for the lack of playlists... it's so much easier for me to organize my videos in my Academy, so I build them out there. Thanks for watching my videos... I really hope they help!! :)

[@hectorjconde9518]

Thanks a lot! you are a great teacher! Blessings for you and your family!🙏

[@omarorchid]

i really really like you. when i don't understand something i search by your channel to choose it specially for you. your explanation is super great

[@kristakingmath]

+Hosam Shawky Wow, thank you so much! I'm so glad you I've been able to help!

[@crashhappy7296]

10 years later, and still some of the best upper level math videos ever made.

[@kristakingmath]

Thank you so much! :D

[@pablo5956]

I may sound like a nerd, but I'm kind of sad that tomorrow I take the last math test of my life. I truly appreciate you taking the time to break these concepts and problems down step by step. I wish nothing but blessings from God on you, and I pray that his grace reign on your life even after you take your last breaths on this Earth! Thanks so much!

[@kristakingmath]

Thank you so much, Pablo, I'm honored to have been able to help along the way! I hope the test went great. And even though you're done, I hope maybe you'll keep playing around with math in the future. Just because you're not in a class doesn't mean you can't keep learning and enjoying it!

[@JAYVEENable]

This video is incredibly well made! Thank you

[@kristakingmath]

+Jeevan Ubhi Thanks! Glad you liked it!

[@kristakingmath]

Glad I could help! Any sketching software. I use sketchbook, but you could also use something like photoshop. :)

[@kristakingmath]

Hahaha, you're welcome! Sorry that things are slow sometimes, I definitely get that. But glad they're helpful when you need them! :)

[@kristakingmath]

I definitely plan to it. :)

[@onslaughtftw]

i never comment on videos but i have to let you know how helpful and awesome your videos are, thank you so much, such a valueable resource for me! god bless : )

[@kristakingmath]

If you are already watching videos for a course next semester, then I know you'll do GREAT! Good luck! :D

[@nadjay3274]

OMG! I get it, I get it now! Thank you soooo much! You deserve the money I pay for this module at uni. Please keep up your incredible videos. xx

[@cobelali]

Awesome video and crystal clear explanation. I wish my textbook (Elementary Differential Equations by Boyce and Diprima) was as clear as your explanation. Can you suggest a better textbook for learning DEs? I don't get the 2 thumbs down. This video is perfect.

[@kristakingmath]

Glad I could help! :)

[@rodgermasinde3696]

ooooh good work madam uv just hammered the nail on it's head .God bless you

[@Barcode3210]

you have the best videos on calculus! and i watch a lot of math videos:P thanks so much for this!

[@kristakingmath]

+Barcode3210 You're welcome, I'm so glad you enjoy them!

[@thebilla6568]

BEST MATH HELP EVER. Can't thank you enough. -Happy Math Major

[@kristakingmath]

:D

[@thebilla6568]

integralCALC AND INCREDIBLY FAST RESPONSE TIME. You are unreal.

[@kristakingmath]

I'm so glad it did! :)

[@osgubben]

Hi from Norway! I love your videos! A few months ago, I was a math beginner, now I feel much smarter :-) But I miss a video similar to the introduction in "Overview Video - Solving Integrals", it was such an AHA!-video. A video teaching what differential math is the same way would be very nice. Keep on your brilliant work.

[@kristakingmath]

@herrzyklon You're welcome!! :D

[@kristakingmath]

I'm so glad it helped! :)

[@kristakingmath]

@runa4eva Awesome! So glad I could help! :)

[@aithavamsikrishna5040]

It's so great.Thank you for giving good explanation.

[@kristakingmath]

Nice! So glad I could help. :)

[@Ensign_Cthulhu]

If at any stage you re-do this video, or do further examples on linear DEs, you should ideally provide an explanation of why, in taking the integral of P(x) to obtain the integrating factor rho(x), you are able to ignore the constant term. (I know, but others might wonder.)

[@kristakingmath]

You're so welcome! :)

[@kristakingmath]

@e9h9hoho No one likes tiny text. :) Glad I could help!

[@cathyli5474]

Great jobs explaining the reverse of product rule! Much more clear than patrickJMT's explanation.

[@kristakingmath]

Thanks! :)

[@someone5895]

BLASPHEMY

[@Benimadimyemek]

its wonderful, the best way to understand lectures, thanks a lot

[@kristakingmath]

+Burak SENOL You're welcome, I'm so glad you liked it!

[@Zevargan]

Thank you very much certainly helped a lot...:) Btw what software are you using?

[@herrzyklon]

Magnificent as usual, thank you!!

[@kristakingmath]

you're welcome! :)

[@MrDod9]

At 7:36, you seem to have to have 2 dx-es on the left hand side, was that supposed to happen? if so, could you please explain as to how? slightly confused about that... Nevertheless; you explaining is very good and the pace as to which you explain is nice as well :)

[@GaGovic100]

your videos really help me alot. Thanks. I hope you can upload more application videos on differential equation. :)

[@kristakingmath]

You're so welcome! :D

[@anzatzi]

awesome boardwork. great presentation--as always

[@kristakingmath]

Aw thanks! :)

[@Ditiro100]

from now on call me Einstein of differential equations...this helped a lot thank you.

[@mohamadd1254]

thanks for these awesome videos ..you are doing a great job…just a couple of comments ..please present your videos in a sequential order and please provide the rationale for the derived formulas …learning to solve math problems mechanically is very easy however in my opinion the most important questions for learners are how have mathematicians come up what these formulas in the first place??? and where can I apply them? If learners are given the answers to these questions , solving them would be a piece of cake ..thanks a million!

[@kristakingmath]

Thanks Mohamad! If you check out the playlists on my channel, you'll find a lot of the videos in sequential order. And making videos about formulas and their proofs is definitely something I've thought about doing.

[@RanBlakePiano]

Love your videos .this particular one needs louder audio .thank you lessons great

[@lindsaychewe8583]

Krista wow! You’re a Math Godess :) Thank you!

[@kristakingmath]

:D

[@junaidnaeem4637]

I did understand everything and followed through it but I am not taking this course yet I will be taking this course next semester. I hope it is going to be ok.

[@kristakingmath]

So true!! :)

[@kristakingmath]

awww thanks!! :D

[@Kev96H]

wow this was so well explained, helped me a lot! Thank you!

[@kristakingmath]

I'm so glad I could help!

[@kristakingmath]

you're welcome!! :D

[@runa4eva]

Thanks this has really helped me out!

[@arvindgaur5067]

I love your videos just perfect, some of them are private - how can i watch them?............thanks for the great effort.

[@kristakingmath]

Awesome! :)

[@JohnSAN51187]

Wow, why can't I have you as my diff eq teacher?! Thank you for this! Love how you explain each step!

[@kristakingmath]

I'm glad I can at least help through the videos! :)

[@naajix]

i was thinking the same John lool... beautifully explained. Thank you

[@kristakingmath]

naajix You're welcome! :D

[@kristakingmath]

hahaha awesome!! you're welcome! :)

[@4EverChrist7]

AWESOME!! It helped so much!! Thank you!!

[@polishhammer1992]

This was so clear! I understand it now! Thank you very very much! *hug*

[@kristakingmath]

Good luck tomorrow! :)

[@aleksandarjankovski6542]

Dear Krista, your explanation is simply superb. Brava! Why are you not completing your PhD in math?

[@kristakingmath]

Thank you! I just don't have any desire to do a PhD right now. I like my job too much! :D

[@amanthakur2434]

Thank you so much for making simple to understand math.... Can you suggest me any channel for physics?? If possible than help me please And thanks again

[@elijah4606]

Hyperphysics is a helpful website for physics. hyperphysics.phy-astr.gsu.edu/hbase/hframe.html Georgia State is the source.

[@kristakingmath]

@gporter9214 Yay light bulb!! So glad it helped!! :D

[@ghulamyahyayousufi4363]

in the first i am so thankful of your beautiful videos they are really help full your are awesome modem

[@kristakingmath]

+ghulam yahya yousufi I'm so glad the videos are helping!

[@lschan9242]

Hi there . I had a problem on how to determine whether a differential equation is linear or not . For example , y'' + (y')^2 +1=0. Why this equation is non linear ?

[@ghulamyahyayousufi4363]

Hi Krista I have a little request from you should you upload some videos about Riccati Differential equation or some examples with their solutions. :)

[@kristakingmath]

+ghulam yahya yousufi I'm hoping to get to more DE stuff in the future, but right now I'm working on a couple of other projects.

[@sfnaidoo]

OMG MARRY ME! I like your tutorial... your nice looks and voice are pretty much bonuses :)

[@GaGovic100]

you're very kind...that'l be great thanks

[@cdog9991]

THANK YOU THANK YOU THANK YOU !!

[@crazymixist]

At 8:53, doesn't it have multiple answers? i mean i would have divided the right hand side by e^3x, or applied natural log to cancel out the e^3x and divided by 3x

[@kristakingmath]

+crazymixist There are multiple ways to get to the right answer. You're correct that you could divide by e^(3x), because that's the same as multiplying by e^(-3x). You'd get the same answer there. It'd be more complicated to apply a natural log, but the point is, there's only one answer here.

[@khalisultani459]

this is so clear very very thanks

[@kristakingmath]

+khali sultani You're welcome, glad I could help!

[@TheBN6]

In the original equation, instead of having y to the first power, what if you had y to the second power? How would you go about it that way?

[@ahmadtahan500]

u make it seem sooooo simmmpplleeee ! thank u soooo sooo soo muchhh !! :D

[@kristakingmath]

you're welcome, i'm so glad it helped!

[@anzatzi]

Perhaps you cover this on your site--but I am surprised it is never covered why this works. Its not terribly difficult to see--but it is interesting. Mostly I am disappoionted with differential eqs as a subject--its collection of analytical recipes for stuff you really have to solve numerically. I am impreseed with cleverness of it. your vids are great. bye

[@jokertangotj7397]

I'm looking for a video that explains this formula to find the integrating factor using e^integral formula you have in the upper right. do you have a video like this? Does is work for any differential equation? I'm trying to understand this concept.

[@kristakingmath]

+Joker Tango That integrating factor only works for linear differential equations, which are DEs that have the exact form as the one in this video. I don't have a video for it, but the top part of this page gives an excellent proof for the integrating factor: tutorial.math.lamar.edu/Classes/DE/Linear.aspx

[@araswali4889]

a little bit late but, best differential equations help on the internets