Change of Variables, Homogeneous Differential Equation (Example 2)

In this video, we continue exploring homogeneous differential equations using a change of variables.
​Using a change of variables we allow us to simplify the differential equation and find its general solution. This example builds on the principles introduced in the previous video and provides a deeper understanding of how substitution can turn complex equations into separable ones. Follow along as we break down each step of this advanced topic.
What You Will Learn:
How to identify and approach a complex homogeneous differential equation.
How to apply a substitution in a differential equation.
Step-by-step process to simplify and separate the differential equation.
Finding the general solution for the given equation.
Perfect for students studying differential equations, advanced calculus, or anyone needing a detailed walkthrough of solving homogeneous equations.
If you find this video helpful, don't forget to like, comment, share, and subscribe. Feel free to ask questions or share with classmates, teachers, or anyone who could benefit from this lesson!
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[@Nyambose271]

PatrickJMT needs to be on the hall of fame!

[@jaymagnus154]

A tip: watch series on flixzone. Been using them for watching a lot of movies during the lockdown.

[@kamdynkellen5398]

@Jay Magnus yea, I've been watching on Flixzone for since november myself =)

[@DeLuini985]

Thanks man, this helped a lot. I finally understood how to scan over this type of ODE to see if I use the v=y/x substitution. Seeing if the numeral and denominator have the same powers overall.

[@AsyrafD]

i wish more people are willing to do this kind of free youtube tutorials, really helping me

[@yuhoseok47]

Thanks a lot, Patrick. You've been my grade saver since high school..!!

[@PinoyPower91]

Thank you so much. My teacher did not explain this well at all, and now I understand how to do this kind of problem thanks to you!

[@alwayslistening4444]

Your videos are truly a treasure to every student! Thanks so much for this very clearly delivered content.

[@ErikDominguezTheWizard]

You are a savior. helping me learn this a day before my exam :)))) Bc my professor is simply not good at explaining lol

[@kksal4375]

I have a quiz today and I was initially so confused till I watched your video....Now I'm confident for the quiz....Thank you so much!!!

[@svennlathrop3450]

Thank you! It helped me a lot. My prof did not explain this clearly. Thanks, now I understand.:)

[@TheCamille1818]

Thanks patrick. i pass now my calculus 3. and now im watching this, i think im going to pass this subject as well. :))

[@jeromecuz348]

The best teacher just keep on feeding us with your knowledge, more examples and more lesson :D

[@nurulaini2112]

Ur solution quite different with my lecturer, but i found out yours are much more easier for me :')) thanks a lot !

[@norman191181]

malaysian lecturers jarang jumpa yang ajar ni terus faham :')

[@DarkCeremony]

Thanks Pat, I learned something new today :)

[@powertube5671]

Great job on this and the previous video! Thanks!

[@ahmedarshad6980]

which is the method to solve homogeneous differential by substitution like y=vx or by integrating factors or that we can solve by both methods?

[@ameer090788]

Thank You so much your work is really appreciated

[@tonyzwane1029]

thanks a lot patrick

[@mercychoka2636]

Thank you sir🤗

[@rdyjur]

Thx again Pat !

[@jasonting6077]

can we still use the change of variable technique if the differential equation is not homogeneous?

[@free2beZebra]

Thank you for your vids

[@smath82]

How can I ever thank you Pat??

[@seemasood3840]

why are we dividing and multiplying by x^something and why not y^something

[@Goods1456]

Why we multiply by tan in both side is their any reasons.please tell us ❤️❤️❤️

[@sherevanalhamy9898]

You are awesome!

[@ryu921022]

thanks so much u r the bestest=D

[@layrapetyan3324]

I don't think you can take tangent because argtangent is between -pi/2 and pi/2 and taking tangent changes that so it's not a legal move) P.S. Thanks for the video!

[@TopLobster9975]

I was wondering why he used the arctan identity for 1/[(v^2) +1] instead of sticking with the natural log since we weren't identifying the use of trig functions at the start. I don't know.. I'm not that great at this stuff yet... at all. Definitely threw me for a loop.

[@TopLobster9975]

Wolfram gives me nearly answer for this problem, but it states the ln|x|+c as simply log|x|. I was confused at first.

[@orainethompson7017]

Your great bro

[@ramiz856]

4:20 he called lovely stuff, it just made me Loved maths :D

[@poorman4009]

I don't understand your point

[@marflage]

@@poorman4009 What Patrick pointed to is not lovely at all. It kills everyone to simplify stuff. His comment is sarcastic

[@dr.engineering201]

Patrick I need your help wit a differential equation. I am struggling to solve. Could you help?

[@Mega2Sakaura]

what if I had something like sin x^2 or e^-2x , what do I consider the power to be?

[@martygarcia839]

Ok

[@0bserver00]

you need different rule and usually substitution method . you need to use identity for trigo problem, for example (sin^2X=1-cos^2) then (sub cosX= u) and (-sinX=du) hope this helps

[@luqmanhakimi3003]

Thanks..😄

[@omarallozi1437]

you should take (y) a common factor and then cancel it

[@mohammadyousefdeebzahran1265]

please can you tell from where he put the tan in the equation (*- *)

[@El650Jefe]

mohammed zahran he wants to get y by itself and in order to do that he has to somehow get y/x out of arctan. One way you can do that is by taking tan of both sides because tan undoes arctan.

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adamın dibisin :D

[@brsznl]

sukunu verdim karsim

[@mohammedal-sharafi7001]

i still watch it from 2019

[@imperialrecker7111]

2020 quarantine man

[@raiyreroland9645]

Bruhh, 30 minutes before midterm.. RIP

[@TheCoolman5500]

Amazing wooooooow

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woooooooooooooooooooooo nice

[@LazerJuiceTV]

you say "again" a lot :P

[@tonyd228]

No

[@cbaker1514]

I will never subscribe to studypug..... sry off topic