The Key Definitions of Differential Equations: ODE, order, solution, initial condition, IVP

[@mathflipped]

Great job! You have an excellent presentation style, Trefor, and high production quality. Congratulations on getting an official sponsor!

[@DrTrefor]

Thank you very much!

[@wakeawake2950]

Congratulations sir on getting an official sponsor.

[@DrTrefor]

Thank you very much!

[@vedantkulkarni6971]

Thank you for explaining everything in such detail. My calculus professor keeps teaching us the formulae without explaining the concept behind it. I really loved this. Thanks a lot.

[@BoZhaoengineering]

ODE is fundamental for STEM. thank you for your intro. ODE is the foundation that you must have to understand PDE or/and engineering mathematics.

[@BrittniHamilton]

Thank you so much for this video and playlist. It is going to save me this semester!

[@aselim20.]

I watched it and I took notes.

[@_B1A]

Congratulations on the first official sponsor!! I have a differential equations finals next week so I will definitely need to check out the app

[@DrTrefor]

Good luck!!

[@eammonhart8338]

Great video, but there's a typo at 5:39 where the 4 should have been multiplied by 3 to give 12. Love the channel

[@aidenmiller3832]

The 3 is there, I think he just kept them separate to better show that it still follows the formula y” - 4y’+3y=0

[@svetlanapodkolzina1081]

This was an excellent lecture

[@DrTrefor]

Thank you

[@actualBIAS]

Seriously, I don't know what to say. Thank you. Making knowledge open source and teaching people in this enthusiastic style like you do is a gift to humanity.

[@toktok5774]

Taking dif eq this upcoming semestre. This is just what I needed. Thank you!

[@DrTrefor]

Awesome!

[@nexevolsegaming]

Love from India bro ❤️💓❤️ Ur teaching style is amazing 💕💯 Loved it 😍😍❤️

[@sarvasvkakkar2545]

Awesome explanation sir!! Looking ahead for your next video🔎👀

[@enamoradadelavidaa]

Thank God I found this. you literally saved my life.

[@khsulaman]

Please make a video on the degree of the differential equations. ( define, not define, polynomial representation, etc) Thanks for the differential equations series.

[@rayannzakhia9372]

“So, there is a infinite number of solutions to a ODE but don’t worry! It gets more complicated”

[@daivagya-7424]

A month ago I was thinking ... Why he is not getting views. Now I know th answer that he is the one and only teacher that goes into too much depth and details .Many lost the concentration while he is explaining. They want only formulas and quick recap. That's really sad.😔😔😔 He should get the more audience. He is tremendously knowledgeable.

[@vedantkulkarni6971]

My calculus professor just teaches the formulae and procedures and never explains the logic behind it. Whenever I ask him any doubt he just says its not in the syllabus or just stick to the formula. Super Annoying. Thanks to Dr. Trefor, we can learn about all these things in detail.

[@mohamadbussins2932]

NICE ! 👍

[@pythonsob5271]

Sir please come up with a series on Numerical methods for ODE & PDE.

[@tejasvibirdh4583]

Explained marvelously and really helpful. Great Job!! Keep it up!!👍 waiting for other videos also (other topics)

[@podiac]

A great explanation simplified and clarified such an elegant way...

[@DrTrefor]

Thank you!

[@BHuman2024]

Professor, I am waiting for your PDE course❤️. Hope that would be fantastic like these courses.

[@chg691]

Thank you sir for the excellent presentation bt plz give me examples or such cases in our real life in which we've to utilise the concept of DE

[@DrTrefor]

We’ll see a lot in this playlist, don’t worry!

[@chg691]

@@DrTrefor Ok sir, I'll wait

[@continnum_radhe-radhe]

Thanks a lot sir 🔥🔥🔥

[@malo270]

Why is everything just complex

[@kiddjmadd]

Maple camera button is sick!

[@DrTrefor]

Isn't it cool? I was pretty happy to support this one:)

[@RickRudy]

FOR FREE???? FOR FREE???!!!! This man is a SAINT.

[@l-gzy7400]

saving degrees for 3 years now

[@fredsmhmd8105]

Loved it.keep them coming🖤

[@DrTrefor]

Thank you! Will do!

[@anupamkumar915]

best visualisation of the concepts ❤️

[@PiniiXever]

holy shit congratz for the sponsor

[@Nhan12031995]

I love the maple app, it's wonderful to solve anything

[@DrTrefor]

That’s awesome!

[@RichardJohnson_dydx]

Thank you, your videos are always so useful this semester.

[@PerplexedGibbon]

What is y dependent on? t? and why is that?

[@apoorvvyas52]

Dr. Trefor, please also cover solutions to system of odes in this course

[@DrTrefor]

This is coming up soon in my math modeling course actually:)

[@hrkalita159]

d(ln(x))/dx ,x=0,,,love to you😁

[@georgesadler7830]

Professor Bazett, thank you for explaining, the key Definitions of Differential Equations/ Ordinary Differential Equations. Differential Equations is used in many places on planet earth. Many courses in Sciences and Engineering uses Differential Equations.

[@j.o.5957]

Question to self: why is it 3t and not 2t? I'm assuming that it's because C_2e^3t solves this, while e^2t doesn't.

[@suhailawm]

Gd evening prof. Pls give me ex. For bijection from even integer to integer.

[@DrTrefor]

f(x)=x/2

[@suhailawm]

Sorry Proff. I made mistake Positive even integer to integer

[@Parknparty]

Maple app works great on my Android phone!

[@DrTrefor]

Nice, glad to hear it!

[@EmilioS-ic6zm]

Thank you so much !

[@ΚωνσταντίνοςΛαζαρίδης-ξ9ι]

Thank you !

[@graceliu5204]

thank you so much professor!!! you explained these concepts better in 10 minutes than my professor did in an hour :') thank you!

[@DrTrefor]

I'm so glad it helped!

[@tomerkozokingandelman3915]

saving my physics ba

[@-NguyenDuyTanA-mh1db]

i didnt got it at 8:09 y^(n)=f(t,...) where did the t comefrom

[@aidenmiller3832]

t is just an arbitrary independent variable, imagine it as X if that helps you out

[@svetlanapodkolzina1081]

Thank you!

[@andrewfranzone989]

Thank you man

[@abhishekthakre1570]

Superb ❤️

[@bhathiyaranasinghe6637]

🔥🔥🔥🔥

[@soumyadyutinandy5119]

first view and comment!

[@DrTrefor]

Nice! I think this is your first "first"!

[@KK-rg3nj]

yay!!! you got a sponsor! kudos!

[@DrTrefor]

Thank you!!

[@sajjad213]

Please teach singular solutions and why a singular solution is an envelope of family of curves. Thank you.

[@DrTrefor]

This will definitely be coming up in the series!

[@dulakmandal6157]

Beautifully explained

[@DrTrefor]

Thank you so much 🙂

[@schoolmaths6051]

Thank you doctor!

[@DrTrefor]

You are welcome!

[@MathAdam]

Glad I found this playlist. Enjoying it.

[@DrTrefor]

Glad you enjoy it!

[@queenisforever1]

Love your work

[@DrTrefor]

Thank you so much 😀

[@r.m.shasikarathnayaka4107]

dr. Bazett you are great teacher. I proud to be a student in your youtube channel

[@DrTrefor]

Glad to have you!

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Most seamless ad of all time.

[@mohammadfallahzade2110]

Excellent

[@DrTrefor]

Thank you so much 😀

[@Alannnn14]

Excellent!

[@DrTrefor]

Thank you! Cheers!

[@u2coldplay844]

Could you please also recommend some textbooks or reference books for your other courses? thanks in advance!

[@DrTrefor]

For discrete math I always recommend this open source one: discrete.openmathbooks.org/dmoi3/ For calculus i use thomas: media.pearsoncmg.com/cmg/pmmg_mml_shared/mathstats_html_ebooks/ThomasCalcET14e/page_i.html

[@u2coldplay844]

@@DrTrefor Thank you very much, It's a blessing that we have you as a great beacon guiding on the road of learning math.

[@playitback-os7mh]

Top!

[@DrTrefor]

Thank you!

[@DrTrefor]

Thank you!

[@sepehr11235]

Your style is fantastic!

[@DrTrefor]

Thank you!