Oxford Calculus: Solving Homogeneous First Order Differential Equations

[@TomRocksMaths]

Practice your new skills in solving homogeneous first order differential equations with this FREE worksheet I've put together in Maple Learn: learn.maplesoft.com/?d=DUINFSISHMOGMUPPNNHMPGFMBJLHGNFJKUJIEJDKMPLKENKNBJMSGUKKALJRPRIQEKLFMONSGSKHAGJRALEGKPFOHJFJLTEODUHS

[@sachamoser8291]

Loved how you teach Math!

[@underthetable2747]

I will be honest, Math in any form was never a strong skill for me, but this is fascinating when you’re high. Love this, excellent work.

[@paulbaker916]

It's because you go to the effort of writing neatly and take the time to explain & write down every step you go though that your explanations are so clear. It's too easy to skip bits when you know what you're doing however you properly teach the subject, and that is the patience those in the know often lack. Good job Tom. Much appreciated.

[@TomRocksMaths]

Thanks Paul!

[@abdullahjawad7131]

Thank you so much, still in awe of how well you explain things. Patiently waiting for your promised linear algebra course videos!

[@TomRocksMaths]

Coming January :)

[@KazACWizard]

you defo deserve the title of prof not only bc of qualifications, the way you orchestrate the solution with such detailed explanations really makes you on another level. i will be trying to get into oxford and id be very happy to have you teaching me any day.

[@TomRocksMaths]

Wow, thank you!

[@mathswithmrzuber1259]

Like WOW! So funny how you get trapped crouching down in the bottom right corner of the board - happens to me all the time. Thanks for the video.

[@TomRocksMaths]

And it would still happen if I started writing further to the left

[@ikocheratcr]

@@TomRocksMaths Board always have the tendency to get smaller as one writes... Happens to me on notebooks too.

[@ZedaZ80]

@@ikocheratcr didn't that happen to Fermat or something?

[@ikocheratcr]

@@ZedaZ80 "Yeah" Fermat, "I do not have space on this border to write the whole proof" ...

[@mouse8302]

I needed this channel 3 years ago during my Maths degree, still good to watch and remind myself how to solve differential equations again

[@ayrtonteixeira6144]

Nice video with incredible explanations. I start taking a differentials equations class after holidays so it’s nice to see a sneak peek of this class and being able to understand everything you did. But oh my there is so much room for error with that amount of alegrara in one problem. Nonetheless cool vid!!!

[@oldadajbych8123]

What impresses me is not that you know how to do it, but you haven’t made any mistake!

[@mathsandsciencechannel]

Nice video Tom... Great work

[@itsreeah2663]

Hello again!!!!😄😁❤️❤️

[@mathsandsciencechannel]

@@itsreeah2663 Hi

[@itsreeah2663]

@@mathsandsciencechannel *Science and maths hugs*

[@itsreeah2663]

Happy birthday Tom

[@owenyates6046]

Every time Tom says Hello maths fans I feel like I should click off because I am absolutely not a maths fan. Only maths channel I found to be fun.

[@TomRocksMaths]

sounds like someone might actually now be a maths fan to me... :p

[@itsreeah2663]

Well I am A maths fan so I find it kind of adorable

[@itsreeah2663]

@@TomRocksMaths hahahahaha, ha

[@iteerrex8166]

Would be cool to go back in time, and show Newton what he started 👊😄

[@shaohongyu7721]

At 2:28, I know you got from x dv/dx = f(v) - v To 1/(f(v) - v) dv/dx = 1/x I understand this part. However, To get from 1/(f(v) - v) dv/dx = 1/x to ∫ 1/(f(v) - v) dv = ∫1/x dx Aren't you just integrating with respect to dx and using the rule of integration by substitution on the left, i.e. : 1/(f(v) - v) dv/dx = 1/x Integrating both sides with respect to x, --> ∫ 1/(f(v) - v) dv/dx dx = ∫ 1/x dx Applying integration by substitution, ---> ∫ 1/(f(v) - v) dv = ∫ 1/x dx You said that we can multiply up by the dx and treat it like a fraction. But isn't the differentiation operator an operator, meaning that it can't be treated exactly like a fraction?

[@shaohongyu7721]

Oh oops sry, should probably have watched your 1st vid on separation of variables first, just realised you explained briefly about this over there

[@scoutcel5157]

HK DSE math paper , need help with them , please make a video abt them, it would be well appreciated thank you

[@TomRocksMaths]

added to my list - thanks for the suggestion :)

[@thomasdickens4846]

Smashing video!

[@erikstanton3908]

I believe you made a mistake when you rewrote the board to say -5ln(2-v). It was negative because of the order switch. On the earlier board, it was correct in saying -5ln(v-2).

[@TomRocksMaths]

Both are in fact correct as we take the modulus when we integrate to get ln

[@Happy_Abe]

This solution also assumes 2x-y is not 0 to be able to divide by it later

[@TomRocksMaths]

yes indeed!

[@matthewgiannotti3355]

Will you please make some maths running shirts?

[@TomRocksMaths]

interesting proposal...

[@matthewgiannotti3355]

@@TomRocksMaths :)

[@IanWilkinson]

Why did (v-2) change to (2-v) @ 11:08 ?

[@TomRocksMaths]

When integrating 1/x the answer is technically ln(mod(x)) so you can decide whether to write the integral of 1/(v-2) as ln(v-2) or ln(2-v). The choice I made was different to the calculator but they are of course equivalent. I purposefully left this out of the edit as I felt it overcomplicated things.

[@ioheil801]

so what is homogeneous in the general case of differential equations?

[@gamerdio2503]

A linear homogenous differential equation is one that is a homogenous function of the unknown function and its derivatives For example, xy'' + 2y' + cos(x)y = 0 is homogenous, but xy'' + 2y' + cos(x)y = f(x), f(x) ≠ 0 is inhomogenous A homogenous function is a function f(x, y, z, ...) such that f(ax, ay, az, ...) = a^n f(x, y, z, ...).

[@itsreeah2663]

Why is x always used in maths?

[@itsreeah2663]

If you love mathematics, reply to this comment to get a hug 🤗

[@luisramrod9121]

Who said rock stars don’t know maths? 😊

[@TomRocksMaths]

preach

[@revan2549]

I miss the days that my brain could solve this

[@MrBenjie1992]

great just differently using 60 to 75 equations...

[@waitandbleed2870]

i vomited it on the paper in my engineering calc class and i dont understand it since then honestly

[@soccerbels7947]

Can't wait to start calculus 3 hhhhhhh

[@TomRocksMaths]

it's a lot of fun!

[@HardikKundalwal]

sick tattoos ngl

[@HausofKinney]

Exhausting >.

[@andrewgonzales1359]

Is he gay? Or am I imagining this?