Differential Equations (KristaKingMath)

[@Nathanielnimtz]

It honestly boggles my mind that these 60 year old professors who have been teaching this stuff for God knows how many years haven't found an easier and more clear way to explain the topics they teach. Your videos clear up every question I have in an easy to understand manner. You're awesome, keeping it up and thank you for making these videos!

[@kristakingmath]

Thanks for the feedback. Some like it this way, others seem to like just the chalkboard. At least there is a mix of both. :)

[@kristakingmath]

it makes it easier to evaluate the integral of both sides. later is calculus we learn how to integrate a function that has multiple variables inside the integral, but people usually don't know how to do that at this stage. for that reason, we separate the integrals so that we can integrate the left-side with respect to y and integrate the right-side with respect to x. :)

[@kristakingmath]

@EvaSlash You can do it either way! :) If you use power rule though, as I did, you just need to make sure that you apply chain rule, and, when integrating, divide by the derivative of of what's inside the parentheses. In this particular example, you'd use the power rule as I did, and then divide by the derivative of y-1. The derivative of y-1 is just 1, which is why I didn't mention it here. If you don't feel comfortable with power rule, then definitely just stick to substitution. :)

[@kristakingmath]

I'm so glad I can help! Thank you so much for the comment and support. :)

[@kristakingmath]

@ploopedoop Yep, you're absolutely right, just trying to simplify things as much as possible. Thanks for the great comment! :)

[@enyapffoeg]

I'm also going for my Bachelor's in EE and let me tell you, you have helped me tremendously in Calculus. I'm not in Differential EQ or Linear Algebra yet, but when I get there, I'll sure look you up. I'm sure I can speak for all when I say, we're very much appreciative...

[@kristakingmath]

you're so sweet!

[@ptyptypty3]

LOL, WOW, Hi KRISTA.. I just bumped into this VIDEO and I had to check it out.... hard to believe this video is coming up on 8 years ago!!.. hmmm a white board, resting on a Couch and you sitting on the floor... BIG SMILES... talk about paying your DUES..... Thank you for all your videos... they're truly a gift to us knowledge hungry students for life... :)

[@mu.makbarzadeh2831]

Thank you so much! You have helped us so much every time! You are our best teacher!

[@kristakingmath]

You're welcome, I'm so glad the videos have been helping!! :D

[@bilaljudeh8862]

6:52 that smile got me good man...

[@kristakingmath]

I hope so!

[@kristakingmath]

@redrum41987 I'm sorry, I don't have anything yet on Linear Algebra, but I'm adding videos as fast as I can! :)

[@zachydrogeo]

Nice to see a little home made video from when your channel was in its infancy. Look how far you've come!

[@kristakingmath]

Sooooo far! :D

[@mohmd252]

I am Arab man, from Saudi Arabia, my English is weak, studying at the Faculty of Mathematics at the third level, I have learned from you too many things helped me to be the creative students in math, I tell you from the bottom of my heart thank you thank you thank you thank you thank you thank you thank you thank you thank you the size of the sky.

[@kristakingmath]

Thank you so much! I'm so glad the videos have been helpful and that you've really been able to use them, it makes me so happy!

[@xoxoYUMoxox]

LOL at her cute hi in the beginning! She is just so awesome & helpful!!!!

[@kristakingmath]

:D

[@ploopedoop]

@TheIntegralCALC Well whenever you integrate any function, there should be a constant left over. There would be one on the left, c1, and another on the right, c2. So when you subtract c1 from c2, it would create the constant C. It shouldn't cancel, since both constants can be different and probably are. But I see that adding C only on the right side saves that step.

[@liftoff5164]

Simple, straight to the point, clear....very helpful, thanks

[@kristakingmath]

+Jeremy Flores You're welcome, I'm so glad it made sense!

[@kristakingmath]

No, I went Notre Dame and majored in psychology (but obviously love math.....just didn't realize how much at the time :)

[@kristakingmath]

You're welcome! Glad you like them. :)

[@shakilkhan4306]

Yet many more years passing by, your videos still enough helpfull for us. You were extremely mind blowing.💕💕

[@kristakingmath]

Thanks for letting me know that the videos are helping! :)

[@cosmickitty9533]

You are the best! Never stop making videos!!!!

[@kristakingmath]

I'm currently not doing any private tutoring at this point. Sorry about that!

[@kristakingmath]

You bet! Glad you like them. :)

[@kristakingmath]

@PeteyPatt You're so welcome!! :D

[@muhammadariffin8810]

i love how the way u are teaching,its really helping me,i am zero in DE and now i can solve the problem with DE,one more thing do u have inhomogeneous second order linear?because im still get stuck with that one,hope u will teaching for that inhomogeneous second order linear,thank you once again for helping me,wish u will become my real teacher, love u =)

[@kristakingmath]

Hi! One of the best things you can do is search through Amazon and read the reviews on various books. Another suggestion would be to google "Pauls online notes" which is a free resource. He has as a differential equations section that may help. :)

[@kristakingmath]

So glad I could help!! :D

[@VonchkynProduction]

How on earth do you explain these concepts so well? I think I'm learning more than i do at school

[@kristakingmath]

I'm just so glad the videos are helping!

[@kristakingmath]

I haven't personally, but I'm sure it's out there on KZbin! :)

[@kristakingmath]

thanks! i'm so glad it helped... good luck with your engineering degree!! :D

[@kristakingmath]

I have a couple videos here: integralcalc(dot)com / second-order-non-homogeneous-differential-equations/. Hope that helps! :)

[@guaman04]

Excellent video !!!! Please, upload videos showing practical applications of differential equations in economics.

[@JamesOfKS]

Great way of explaining things. even things we should know (but maybe don't remember).

[@kristakingmath]

Thank you so much! :)

[@kristakingmath]

Awww, that's very sweet of you to say, thank you so much! :)

[@peterh.1521]

Exemplary illustrative math lesson in the subject DE is the least one can say. Thanks Krista!

[@kristakingmath]

+peter hansi Thank you so much!

[@briLLiantaz]

Really nice, helpful and informative. Huge thanks for your videos!

[@coolwales1]

Aye! thank you so much. I will check them out. I know that my foundation for this course is very weak but as you said, I will stay positive. I swear, if you are a country like America, there is no way the whole would will not fall in love with us, even Alqaedah. You touch many lives in a totally awesome way. Wishing you live in Chicago! Have a good afternoon :)

[@kristakingmath]

LOL, sorry about your professor, but I'm glad I've been able to help along the way!! :)

[@aminemoumeni835]

Krista King the beautiful math teacher that i have seen in my life love u

[@kristakingmath]

I would also check out first-order linear differential equations, separable (non-linear) differential equations, and initial value problems. you'll need all of those to get a good start in DE. Stay positive, you can do it! :D

[@nadhrahzulkifli8238]

a massive thank you for teaching this , i've seen many videos explaining DE but i did not understand none of them. Greet from Malaysia :))))

[@kristakingmath]

+Nadhrah Zulkifli You're welcome, I'm so glad they're making more sense now!

[@thearchitect27]

You are truly a mathematics muse! Thank you so much for your sincere help, O great one...(bows down in humility)

[@kristakingmath]

lol, i'm so glad it helped! :D

[@thearchitect27]

integralCALC Hey I have a question, I am an architect and studying civil engineering, and I'm alright with calculus, you know, it's not that bad anymore. But what are some practical applications of it in engineering? Let's say which branches of calculus/Differential equations will I ever actually apply in my work, any ideas?

[@kristakingmath]

@MrStratification When you integrate both sides, you should only add C to the side with your x variables. If you added C to both sides, they would cancel each other out, and then you wouldn't be able to solve for C! :)

[@rpmerick]

Thanks for putting those videos up!

[@mattheModest]

Gotta say I prefer the ones where I can see you, makes the videos more personal and, at least for me, makes them more interesting. Not that the other ones are any bad.

[@kristakingmath]

Glad I could help! :)

[@JoshuaBoothCreative]

Thank you for everything. I'm completing my final today for Calc 2. Its been a great ride and you've helped a ton! Without your videos I would have given up last semester on Calc 1

[@kristakingmath]

Joshua Booth Studios I'm honored just to be able to help! I'll keep my fingers crossed that your final goes great! Good luck!!

[@JoshuaBoothCreative]

integralCALC thanks! Your voice is so calming and makes calc seem easy. Im just glad its over, no more calc. I wish you taught Linear Algebra :/

[@CyberFenix000]

Joshua Booth Studios I don't like women... can we get math videos done by lolis, I'm a lolicon and NOT a pedophile. I love lolis, and even more if they would be giving a math lesson. :^3

[@mcgarettsteve9077]

thanks a lot...finally got it after watching your video..a nice and elegant video...thanks again, much appreciate the help..:)

[@ACoroa]

Omg! You pwned that problem! Thanks so much for sharing! :-) Eu curti muito!

[@DrSeaLionMD]

This video made so much sense! Thank you so much!

[@kristakingmath]

You're welcome!! :D

[@kristakingmath]

Thanks for letting me know! :)

[@kristakingmath]

Thanks!

[@aayushmann9743]

❤❤I love to way of your teaching ❤❤❤❤❤ ....it's help to me in pcm exam !

[@EvaSlash]

3:24 when you integrate the left side i see you used the power rule for integration. but i thought power rule only applies to x by itself in an intergrand. Aren't you suppose to use substitution to integrate the left side?

[@julieha2534]

ovule been my go to for my tests. thank you u are so amazing!

[@kristakingmath]

Julie Ha I'm so glad the videos have been helping!!

[@citizenkoehn1]

Nice video! When you divide x^2 + C by 2, can't you just simplify that side of the equation to just (x^2)/2 + C (as any generic constant C/2 could still be represented as C)?

[@saberwingNetwork]

I was wondering the same thing.

[@kristakingmath]

yes, you absolutely could, you're right! :)

[@bazejruba8750]

You took indefinite integral of (y-1)^(-1/2)dy using power rule. In this case it gives us right result, but is that really correct? Shouldn't we solve this by substitution? Again, I know this works in this example but I don't think it will work everytime and it's bad to make bad habits.

[@SkukS]

Nice video :D You don't actually need to divide the whole right side by 2 when you take the 2 over, it just means you will get a different value for C.

[@Mekstee514]

Great video, short & simple! :)

[@nandan435]

Thank you so much for the videos they really helped me with calculus.

[@kristakingmath]

You're welcome, I'm so glad they've helped!

[@kristakingmath]

you're welcome! good for you for going after such a great degree... i know you use A LOT of calculus and differential equations in EE. good luck!! :D

[@quod]

Is it necessary to divide C by 2, since differentiating with any constant will yield the same integrand?

[@kristakingmath]

@MrAbhilash02 :)

[@shalomes2012]

good job and thanks for explaining so well

[@kristakingmath]

Thanks!

[@sunilreddy146]

Can you tell me how i can deduce whether a differential equation is linear - non linear, time variant - time invariant, causal - non causal and other similar properties.

[@renzoandre5286]

Thank you, you're awesome! Just one question, so if we were to plug what we found for y into the original equation, replacing y, then that result would be the derivative of our answer? In other words, what does the answer you got mean?

[@kristakingmath]

The easiest way to think about it is that the answer we got at the end is the "original equation", because it's just a normal equation solved for y in terms of x. Then you can say that the equation we started the video with is the derivative of that "original equation". If we plugged our answer into the equation we started with, we'd have (d/dx)(y=...), and that (d/dx) would be an instruction telling us to take the derivative with respect to x. Good question, and I hope that helps clarify! :)

[@renzoandre5286]

Oh I see, thanks I appreciate the answer!

[@pakhan612]

you really help me to understand the concept

[@kristakingmath]

Glad I could help! :)

[@proveItllc]

you are a genius. Thanks for making it so easy

[@kristakingmath]

+George Sadler I'm glad you felt like it was easy!

[@Captain_Rhodes]

thanks. explained much better than my textbook!

[@MrCameren93]

You're gonna help me pass Calc 2 :) thank you so much!

[@ededdy6630]

What is the reason for separating the x and y on both side of an equation???? if its algebra i can understand but this is for what reason?

[@ddhts]

Nice video...did you hand-pick that prob for neatness, or is it that you just make it seeem soo eazy!? Anyway, about the C constant, it makes me feel uneasy in paranthesis....can you extract it and let it bring up the caboose (or am i just being too neurotic about it)? Thanks

[@kristakingmath]

+Drake Dimitry You actually could if you wanted to, yes. But it's probably best if you stop worrying about it and just let it be wherever it ends up! :)

[@ddhts]

Ok, thanks...i'm good with that!

[@JustSimplySilly]

Have you ever gotten into the higher level classes such as abstract math and linear algebra?

[@kristakingmath]

No I haven't.

[@hasankhanjar-ff3sw]

thank you krista i really hope to meet you oneday

[@eelavan1000]

Can you multiply by dx both side? dy/dx is kinda fraction?

[@completesufficientstatisti7352]

hi...mam ive a confusion about order and degree of equations in trignometric forms ,.,.,,.i mean what would be thw order of : sin(y") + y' + blah! =0

[@alahemy]

y=1 is also another solution!

[@kristakingmath]

At least I can help on KZbin! :)

[@coolwales1]

Help Help Help!!!! I wish I knew you personally but anyway, I have been out of school for a very long time like 6 years. It feels like I never did maths before. I was studying engineering and now going back. I am taking differential equation this semester which I must get an A or B minimum as required so that I may be able to continue. I have relearn some basic integration from you like substitution method and integration by part. Are these good enough to cope with differential equation? Advice!

[@harivikraman9821]

I have a question: when you integrate both sides after setting one variable on each side, don't you have to put a C on the y-side as well as the x-side, or no?

[@kristakingmath]

technically yes, but the putting C on both sides will always result in consolidating both of them to one single C value, so instead of doing the extra steps every time, i just add C to the right side.

[@harivikraman9821]

integralCALC Oh okay. Thank you.

[@kristakingmath]

you're welcome!! :)

[@kristakingmath]

You too! :)

[@PunkSkaful]

OMG! I love you!! Thank you for this ♥

[@아내지민의]

does it change everything if we find x than y?

[@kristakingmath]

thanks!! :)

[@kristakingmath]

Good for you! I think the math minor will definitely help you with engineering. Good luck with your degree!! :D

[@coolwales1]

Thanks for the response. I am sorry if I am starting to be a pain. I really appreciate your work ... I have questions if you are taking questions :)

[@fawzyhegab]

nice example , thanx for your vids :)

[@macmos1]

I would say cuase they're so advanced in the subject and have a deep understading for underlying theories its sometimes hard to simplify.

[@amoooorh1000]

i am in a college so i have some problems with this differentiation and i take these with another way..so... i want to get your mind just for a few years plzzzzz --- hhhhhhhh__ you are amazing keep going D/ awesome

[@siyahdeniz]

You are, with a high level of certainty, extraordinary :) Something beyond of limits in lots of different spaces :)

[@kristakingmath]

You're so sweet!

[@jakey2938]

what kind of age would you be doing things like this?

[@teena139]

no way! i went to college there! best city ever :] and where were you when i took pre calc in college?! haha

[@kristakingmath]

good! thanks! :)

[@goldensquare4]

Great explanation

[@kristakingmath]

Thanks. :)

[@Priya_92]

This is a great help thankyou so much!!

[@jesuisravi]

Good job!

[@coolwales1]

You are welcome. It looks very tough so far but should I end up not dropping the class and getting at least a "B", I will like to meet you. This is my request :)

[@kristakingmath]

@redrum41987 Aww! Thank you!! :D

[@shylildude]

did you go to ucsc? if so, what was your major?