Linear differential equation initial value problem (KristaKingMath)

[@PathToEntrepreneurship]

I remember 2 years ago when I entered engineering that all I used was PatrickJMT or Khan Academy because I saw that you only had a few videos on calculus. About 2 years later, through your hardwork, you have become my main choice of learning for my differential and integral calculus because of the expansion of your video content. I suggest that you consult PatrickJMT and maybe form some sort of joint venture to combine your content. I really love how organized your lecture notes and videos are. I also like how your lecture notes are very simple and easy-to-read without all the complex notation my textbook uses. PJMT has a lot of useful content and many videos but his stuff really needs proper organization. Excellent work! Keep it up. PS: Since you know how to explain complex stuff into simple words, can you explain to me why textbooks make simple concepts so difficult to understand for students? After all, textbooks are suppose to teach us and not confuse us.

[@kristakingmath]

Wow, thanks for the awesome comment! :) It makes me so happy that you've been able to follow my updates along the way. It's been a lot of work, but a lot of fun as well. I love what Patrick and Khan do, and it makes me happy that I'm able to help in my own way. Even though I haven't collaborated with them, it feels as though we're on the same team fighting for a similar goal. :)

[@danielray5571]

The thing about math videos is that you only need them when you are learning about what they are explaining. Subscribing doesn't really help me because I don't want to have these videos as soon as they come out, I need them only when I search them up. Your videos are amazing though!! Thank you!

[@kristakingmath]

I don't disagree. If searching for what you needs works for you, that's great, I just want the videos to be helpful!

[@asavelanotshweleka2623]

I love this lady she can teach she makes it clear. .this is what I call a lecture

[@SteveMcRae]

When I took college calculus back in the day most of the time it was essentially a matter of going through the motions using things like the product rule or chain rule vice a more detailed pragmatic approach to solving differential equations. Your explanation on why exactly why the product rule works in this type of equation would have been oh so helpful to me years ago! You don't just teach, you explain...and that is something many instructors don't bother to really do. Your videos are not only an excellent resource of information, but they are also "how to" videos on "how to" educate.

[@kristakingmath]

Steve, I'm honored! Thank you so much!! :D

[@Emc4421]

I have always been good at math. I am taking this class at community college and my professor makes it WAY more complicated than it needs to be. To the point where I am so lost. But when I watch your videos I know exactly what's going on and understand how to work my way through the problems. I also like how you throw little things in there which end up helping me alot. For example in this video, you mentioned that the e and the ln have to line up to cancel out. Little things like that help me alot as well. Thank You Krista.

[@bennihannariendo5030]

I can't thank you enough for your concise, direct examples. I search these types of videos a lot. I see all types. you are organized and rehearsed. Those things combined with your excitement about the material is truly what sets you apart. Best math help I have come across. Thank you

[@kristakingmath]

+bennihanna Riendo Wow, thank you so much! :D

[@beriman09]

It's truly refreshing to have someone explain these problems without skipping any steps, your efforts are greatly appreciated!

[@kristakingmath]

I always hated when steps were skipped too, so I do my best not to do the same. :)

[@mickygarcia4251]

Krista, thank you so much for being concise. I think people who make these videos forget that we can replay them when we need to review a part of the lesson.

[@kristakingmath]

+Micky Garcia Thanks for the feedback!

[@GarySaini8]

You are a LEGEND!!! You've literally cut two days of studying down to 1o minutes.

[@kristakingmath]

:D

[@laurencrom]

This is awesome... You explain things so well! This is the best (and only) video that goes through linear differential equations!

[@kristakingmath]

Aww thanks! Glad you liked it! :)

[@madenaarcher9051]

Krista...you are like the Sparkle Glitter Queen of Maths, I love you literally, you make this stuff look infinitely small. Thank you soooooooooo much and you ROCK

[@jackodum9643]

When I listen to your video you make the problem very simple with your nice gentle voice, it just like listen to a very gentle music that is very easy to understand. I have not seen anyone like you before thank you very much. You also have quality website which I recommend people to join.

[@AMLennon]

nice visual upgrade from your 2010 video on same topic. I really love and appreciate the effort you make in ensuring that your viewers grasp the concept. I'm grateful. Thanks Krista

[@Bo_injoom]

Thank you for helping me out last course, and answering my questions, I really appreciate it.

[@travisallen4718]

I'm not sure why so many other professors fail entirely to explain the integration technique used/needed on the left side of the equation after multiplying the integrating factor through... But you deserve a gold star for this simple breakdown. Thank you- thank you -thank you.

[@kristakingmath]

+Travis Allen Thank you so much, I'm glad it made sense!

[@Douggarding]

Thank you so much for this video. You did a great job of simply breaking the problem down into as many steps possible, and explaining each one. Many textbooks and teachers skip over even the simplest steps and I'm left wondering how/why they got from one step to the next. I appreciate you sharing that knowledge.

[@kristakingmath]

+Doug Garding You're welcome, I'm so glad the extra explanation is helpful! I really try not to skip steps in my videos!

[@fritzd2116]

As an engineer that is starting a masters in engineering(22 years after earning my B.S), I find your ODE videos incredibly helpful. Keep up the good work!

[@kristakingmath]

Thanks Tim! Glad they can help. :)

[@keinhsyldio1835]

i did not ever understood math in my school life from secondary but today it is not looks like before my colleague come to me to consulate how to do math so i am proud of you but you my mentor from this video.i wish i were meet you to shake hand each other,wish you all the best my almighty God bless you

[@krissi9183]

You have helped me so much more than my useless professors. Thank you thank you thank you!!!

[@kristakingmath]

You're welcome!! :D

[@hayesmyers2259]

I think the inverse of your equation is most correct.

[@Ahsan17687]

Yeah good explanation

[@kristakingmath]

you're welcome! i'm glad you enjoyed it! :D

[@Jake-rj4tc]

You and PatrickJMT are alot of help, college profs are not worth listening to anymore with these amazing videos.

[@quynh_]

tysm omg I've watched about 5 or 6 other videos on this same topic and I could not even grasp this concept until watching your video. Keep it up!!

[@kristakingmath]

+Quynh-Nhu Dao Thank you! I'm so glad it helped!

[@waltwilliams1770]

Thanks again Krista for the clear explanation. The stuff on the left side after the integrating factor is included I have come to think of as the "un-product rule". This could be a way to better explain why part of the terms disappear.

[@kristakingmath]

+Walt Williams I like that, Walt! The "un-product" rule is a clever way to put it!

[@wroose]

Many thanks for your helpful videos and hard work for the community. I was able to quickly catch up on all the material I missed in class and I'm now much more confident about my calc final. Thank you

[@kristakingmath]

I'm so glad!! Good luck on your final... you'll do great!! :D

[@ddhts]

Awesome...gotta go over that last trick again...it is great to have it in our bag of tricks!

[@kristakingmath]

Awesome! I'm so glad I could help. I hope the test went well! :)

[@byteaesx1373]

As always we can't thank you enough for your work and the time invested on it.

[@kristakingmath]

Aw thanks! I'm glad I can help.

[@Crossfire9211]

Knowing something's all about being able to explain it, simply. Nice job

[@kristakingmath]

Thanks!

[@kristakingmath]

Yay! I'm glad I could help you understand it even further! :)

[@mycutefamily7047]

Hlw ma'am I'm from india I have some prblm in this particular topic of finding initial value can you please help me out ma'am??? Our teachers have as assignment but it's fully out of syllabus for us.. I dnt even know how to solve it please ma'am help me out I need to submit this within 3 days☹️☹️☹️

[@JoliNoelleDavid]

thank you SO much for this! this was so so helpful. i was struggling with this concept for the longest time

[@kristakingmath]

You're so welcome, Joli, I'm so glad it all finally made sense! :D

[@JM995able]

OMG, you are awesome, i've been trying so hard to figure this out more than couple hours, but just by watching this 10 mn videos i did, Thank you!!!!!

[@jchizer]

Thank You so much!!!!! your videos helped me get a 87% on my first test! Your videos are the reason I'm passing Differential Equations. Please post more DE videos if you can they're really helpful.

[@listless32]

Your videos have been so helpful and I appreciate how you share your knowledge with the world!

[@kristakingmath]

Thanks! I'm so glad I can help. :)

[@ethanklimczak5692]

I love your explanations! I can read it from book for an hour OR just watch your 10 min video. :)

[@ukenur2598]

Krista, you could have been a teacher of an university. Thank you a lot for helping people to understand some math topics

[@kristakingmath]

I'm glad I can help!

[@kristakingmath]

you're welcome! good luck in DEs this summer... that's a tough class! :)

[@MrJithoo123]

The video is good. Please also explain the concepts behind initial value problem...integral factor...etc

[@zakariye55555]

THANK YOU for being such a good tutor! By far the best youtube channel on Calculus. You make it easy and fun :D. You just earned yourself a new subscriber! :)

[@kristakingmath]

Aww thanks! :D

[@ianetzwiler3416]

Wow! I am both a long time mathematics tutor and algebra instructor ... Great video!!!!

[@kristakingmath]

Thank you so much!!

[@StatsMedia]

do you have homogeneous first-order equation? -like how to determine if the function is a homogeneous?

[@kristakingmath]

I've got lots of videos on first-order homogeneous DEs. :) You know the DE is homogeneous if the right-hand side is zero! :)

[@GabiN64]

You explained the d/dx dilemma i've been having. I've watched other vids and read books prior to this, but this vid explained it perfectly.

[@kristakingmath]

***** i'm so glad i could help!

[@alwayslit_texting]

AT 1:46, WHEN YOU SAY YOU GET ONE OF THE X'S TO CANCEL, HOW CAN YOU DO THAT WHEN YOU ALREADY HAVE THE 1\X IN FRONT OF THE Y? PLEASE HELP KRISTA :)

[@kristakingmath]

you get one of the factors of x in x^2 to cancel. when you divide every term by x, for that particular term, you get x^2/x, which simplifies to just x.

[@axel39er]

The pulling out D/Dx bit was explained awesomely. Thanks !

[@kristakingmath]

:D

[@axel39er]

I was wondering if you could do any videos on Partial Differential Equations and ODE's constructing Green's functions? thanks so much !

[@kristakingmath]

I'm glad I could help! Thanks for subscribing! :)

[@Neueregel]

Thanks for posting. Ricatti and Bernoulli are also interesting cases of Differential equations.

[@kristakingmath]

Glad I could help! :)

[@Kyleser1BlogspotCa]

That pulling out of d/dx just saved my life! Thanks so much!

[@kristakingmath]

you're welcome! i'm so glad it helped!! :D

[@baykkus]

Thank you! I kind of did know what I had to do, but the fact that half of the equation seemed to disappear out of nowhere always made me feel confused. Now that I understand where everything comes from I feel confident in my ability to solve this kind of problems, and it does make a lot of sense.

[@kristakingmath]

You're welcome Julio! I'm glad it could help. :)

[@ThePharaoh41]

Great video. I'm trying to brush up on some higher level math, but it's been a while. I love the way you break out each step in simple terms. Thanks a lot.

[@kristakingmath]

Thanks! Glad I could help!

[@jr52990]

Currently going through this stuff in Differential Equations class. Taking the sign and using that for the variable (P(x)) helps a lot.

[@kristakingmath]

Awesome, glad it helped! :D

[@noahquinn9703]

4 years late and i still find this video helpful for my Calc midterm, thanks for the video

[@kristakingmath]

You're welcome, I hope your midterm goes great! :D

[@DeathrashWhiplash]

Makes a "differential equation" seem like a cakewalk really. Well done 😊

[@kristakingmath]

Glad it could help! 😀

[@JimCharlesTroy]

Why? Why do I learn this in 10 minutes when it takes my professor ages? Why can't every professor be this awesome and this efficient??? WHYYY?!?!?! God, please make more people like this! :D Thanks! Have my like and my sub!

[@gregoryrichard1765]

Thank you so much! Best math teacher on KZbin!

[@kristakingmath]

Thank you!!

[@steven_grande]

I thought I understood but then I watched this video and you completely simplified everything. Now I really understand, thanks a lot!

[@alechewitt2347]

At 8:05 don't you need to get dx on the right-hand side before you integrate so that you can integrate with respect to something?

[@batman52000]

Just wanted to say thanks for this awesome video. It helped me understand the concept immensely.

[@kristakingmath]

+batman52000 You're welcome, I'm so glad it helped you!

[@NabilClips]

you are so cool and I want to thank you for being my Math teacher during my whole College life. I just love leaning from you.. your explaining is incredible

[@kristakingmath]

I'm glad I've been able to help along the way!

[@mahmudusman2350]

thanks so much ...I just have exams tomorrow and you explained everything in detail ,keep on doing this way.

[@kristakingmath]

Thanks! Good luck on your exam!

[@kristakingmath]

You still had to put in the work, but I'm glad I could help! :)

[@soren81]

Thank you, please continue with the differential equations!

[@blastellesjr.1187]

I watched this video while doing my homework and it was very helpful! Thank You!

[@kristakingmath]

Good idea! I'm so glad it could help. :)

[@BlackLabelActual]

As usual your videos help fill in gaps my math professors leave out, Thank you! Subscribed as well

[@keghushahemen829]

that's prettily amazing. i'm interested in studying here all the time.

[@larrymccartney5633]

question: why do we not add a constant of integration when we integrate the integrating factor - it would produce arbitrary constant a (say) over x?

[@vicangelofabella5191]

This one is a good refresher

[@Gabriela-zf1jy]

Do you think you can do an introduction of the Initial value problems??

[@kristakingmath]

+Gabriela Ayala I can add it to my list!

[@kristakingmath]

Will do, you're welcome! :)

[@Pablo28mr]

Excelente aula! Você explica muito bem. Adorava essas aulas no curso de engenharia elétrica.

[@kristakingmath]

:D

[@Pablo28mr]

Obrigado! :)

[@generalnango]

cool, great video! a lot of the other videos on linear 1st order ode's skip the part of product rule explanation for the breakdown of the left hand side. you didnt skip it, so i learned it! thanks.

[@kristakingmath]

awesome! i think it makes it easier to understand, and i'm so glad it helped!

[@sweetyvany99]

6:20 what happened to the -1/x^2 why did it vanish?

[@kristakingmath]

Thanks so much for sharing your success! That makes me so happy. :)

[@phantienminhthuy3805]

Thank you Mrs. King again, you're the very very very best!!

[@kristakingmath]

You are so welcome!! ❤️❤️

[@StatsMedia]

You are a very good teacher... without your video I will probably fail my Subject.

[@kristakingmath]

I'm happy I can help! :)

[@exambuddyyt7896]

Need help on this. Can you integrate sin x even without the dx? When you cancelled the d/dx you also integrate the sin x on the right side even if you don't have a dx on it. I need help on this. Thanks! :)

[@nrsoft32]

That tricky was one of the best tricky i ever seen :D , Tnx so much , your teaching is really better than my lecturer

[@goveanicolas]

Would you happen to have a video of a initial value problem where you have to find an explicit solution and the interval where it's defined?

[@rigoalhn1]

Hey great video. I am confused in what happened to the 1/x^2 after you pulled out d/dx. thanks

[@SJFredrick]

When taking the integral of the integrating factor, wouldn't it be, -ln|x| not ln(x), what allowed the absolute value signs to be dropped?

[@wawcrates]

I'm not sure if I missed you mentioning it, but are we supposed to ignore the arbitrary constant when you integrated -1/x towards the beginning?

[@kristakingmath]

+wawcrates Yes, you can ignore the constant when you're integrating to find the integrating factor. With these linear differential equations, that constant will ALWAYS end up disappearing later on in the problem anyway, so people tend to leave it out. If you're interested, there are proofs of this online that'll show you why the constant always disappears.

[@kumaranr7646]

Thanks so much!! This helped me a lot with studying for my math test tomorrow.

[@Postcalculus]

Thanks so much. You are doing great work, representing the best of human spirit. May God bless you.

[@GustavoHernandez-ws1gq]

very clear explanation. Thanks for refreshing my memory :D

[@kristakingmath]

+Gustavo Hernandez Thank you!

[@GreenCapElf]

I really don't know how to thank you! I'm so glad I found your videos. You have guided me through my differential and integral calculus courses. Keep it up! vr

[@kristakingmath]

I'm glad I can help along the way!

[@mohfa1806]

hello .....very nice explanation...congrats...one question please : why we ignore the constant of the integrating factor?

[@kristakingmath]

+Mohamad Fakhoury Because with linear differential equations problems, it will always end up canceling out in the end. There are proofs of this online if you want to see one, otherwise, you can just know that the constant of integration will get always disappear, so there's really no reason to carry it through in the first place.

[@mohfa1806]

thanks for your answer....i worked with the constant till the end , and yes it cancelled out :)...thanks again

[@samanthastuart3887]

YOU ARE AMAZING AND JUST SAVED MY LIFE

[@kristakingmath]

+Sam Stuart I'm glad I can help!

[@BkSenko24]

thank you so much baby, helping me with my summer course in diff eq. clear and concise explanation.

[@muhammadhanifansit3144]

this video is very interesting, is there any example that related to trigo + unit circle ? i'm having trouble for that part.

[@Benimadimyemek]

i captured whole points, beyond the wonderful

[@ibraheem3abassi579]

i keep watching this video to remember the solving method. most beneficial video. Thank you very much.

[@kristakingmath]

+ibraheem hanbali You're welcome, so glad it helped!!

[@siyuanthesuper1]

Hello Why can't you just use the equation y= (e^(-p(t))) int (e^(p(t)) g(t) dt + Ce^(-p(t)) isnt that easier?

[@3n7r0p1c]

Is it possible to use this same approach for initial value problems such as, (x+y)^2 dx + (2xy + x^2 -5)dy = 0, y(1) = 1 ?

[@haris525]

hello - great video, but I was wondering isint P(X) = -1/x? sorry my ODE is rusty, but PDE is soild

[@stevelost1950]

Very concisely explained good job keep it up. I wish you were my Calculus professor!

[@kristakingmath]

+Steve Lost Thank you so much!

[@muhammadtaufiq6661]

hi! actually Im still working on my thesis and ofcourse i got problems. can u show a video solve a linear FUZZY DE initial value problem? how to make the DE to fuzzy??? can u share???? pleaseee

[@flyboy068]

Thanks a lot! Really helped with my online class. You've got another subscriber!

[@kristakingmath]

I'm so glad it helped, thanks for subbing!

[@rchiuz01]

Thank you! The d/dx really cleared up my confusion :) keep up the good work ^_^

[@EchoVids2u]

I love you Krista. I finally understand now!

[@kristakingmath]

I'm so glad it could help!

[@dylanvanrooyen510]

Best video for help on linear differential calculus before a test. enough said :D

[@kristakingmath]

Thank you so much!!

[@josephperez3389]

Thanks, very helpful. Been using your videos for 3 years now.

[@kristakingmath]

Aw that's so awesome! Thanks for letting me know. I'm so glad I've been able to help along the way!

[@josephperez3389]

You have helped more than any tudor/professor ive had. And im a senior in an ocean/civil engineering major at A&M.

[@kristakingmath]

Joseph Perez Well I'm honored, thank you!!