The Method of Integrating Factors for Linear 1st Order ODEs **full example**

[@alexfriedman7904]

these two videos on integrating factor may have been the 15 most educational minutes of my entire life, thank you Dr. Bazett

[@rogeliotoribio149]

😢

[@Zeddy27182]

Dr. Bazzet! I've always been grateful to you🙏 As a math student, I have always been beyond amazed by the grandeur of mathematics.😲 It is PHENOMENAL! 💯💫

[@shubhampathy780]

This channel is really underrated

[@DrTrefor]

Ha, I like to think so!

[@03FRK]

Generally don't leave comments but this video just cleared absolutely any and every bit of uncertainty I had with ODEs. Now I'm going to search for your videos on 2nd order ODEs!

[@alperari9496]

interestingly, i saw same topic yesterday in my lecture. He is still better than my instructors

[@Aaron-sr6nc]

This is a great explanation! My professor didn't explain this anywhere near this good and left me so confused but it's so much easier than I thought. Thank you!

[@shmkrar1153]

Thank you so much sir. I was learning about the charging of a capacitor and got stuck at a linear first order ODE. I used this and the previous video to learn how to solve them, and I was finally able to derive the capacitor charging equation myself. Thanks a million from India!

[@Geometiclink]

Thank you. I needed this to refresh my memory.

[@researcher7109]

Dr Bazett, thank you so much. The first video and this video really helped me understand Differential Equations.

[@adrianj9695]

Thanks for sharing this. It cleared up a couple issues I had solving some problems.

[@thejesterschagrin]

Such a clear, easy-to-follow explanation. Thank-you so much! :)

[@deang6763]

first of your videos I've watched, I have an exam tomorrow and was just brushing up on a few niggly bits. This was extremely well explained, thank you!

[@georgesadler7830]

Professor Bazett, thank you for solving Linear First Order Ordinary Differential Equation using The Integrating Factors.

[@darkh1wk244]

Thanks for making this so easy to understand ❤️❤️❤️

[@2pumpchump420]

This video made me angry. I just realized how poorly my professor explains the fundamentals of Differential Equations like integrating factors. I loved DE in undergrad and haven't really enjoyed it in the grad course. I hope your Fourier Series videos can save me. Thanks for the great videos!

[@Leon_George]

If all universites had the teaching abilities you possess, the world would be filled with many fewer dissatisfied graduates, and enthusiastic engineers!

[@chloechong940]

this example saved me, literally

[@WyattVanLoon]

So if the product rule is an equality and a direct substitution for the left side of the equation, why do you still multiply the integrating factor by the right side? Because it is only a direct substitution after you multiply the IF by the whole equation?

[@alexandrachiritescu196]

What you said at 2:25 is not true if it's the derivative with respect to x. Could you explain, please?

[@nebula8763]

right they dont cancel out they add together

[@AnasHawasli]

dude this content is gold thank you so much

[@reececavallo9661]

Great explanation. Thanks, Doc!

[@JonahBouchard]

Idk if you still answer these but at around 2:28 how did you simplify that.

[@zspolt]

essentially reverse the product rule

[@shubhamsatyaprakash54]

Awesome!! Dr.

[@blessingsphwitiko9926]

Useful content that helped alot. i appreciate it

[@bananacheeto1574]

Legend! Thanks!

[@jacobvandijk6525]

@ 0:22 Of course, 1 = y^0

[@atshaamashraf7402]

Great vid mate keep up the good work 👍

[@vanlang9959]

Thank you for this informational video.

[@Tyokok]

Hi why you only use g(x) but not the f(x) ? Thank you in advance for any advice!

[@sumchief]

Nicely explained

[@syabongajele6431]

wow perfect DR

[@dylanpereranba9363]

Hello, I have a quick question. For can you solve a separable non-linear ODE's with methods we use for linear separable ODE's?

[@DrTrefor]

If it is separable, then yes it is solvable always (up to our ability to do the integrals). However, the method typically will NOT be the method of integration factors.

[@dylanpereranba9363]

@@DrTrefor I see. Thank you for getting back!

[@redsword7192]

It was helpful. Thank you.

[@nhaz652]

i still couldn't see it for the product rule. can you explain for me?

[@noahbarrow7979]

Greetings again from nyc! Another awesome video Dr. Trefor :) Got a quick question about some mathsss at the end. I paused the video and tried working the problem through first but when I tried to isolate y and divided the right hand side of the equation by e^4x i got y = (1/3e^x) + C/e^4x. I'm sure this id deliriously minor but I just don't understand how you got e^-4x on the right hand side...

[@DrTrefor]

Greetings! You and I are saying the same thing. That is, Ce^{-4x}=C/e^{4x}, this is the meaning of the negative in the exponent is basically that it puts the same thing with a positive down in the denominator.

[@noahbarrow7979]

@@DrTrefor AHHHH! Thank you so much! This was a case of-"i have been looking at these same numbers for so long that i feel loopy". Thank you for being so patient and clearing that up for me!

[@noahbuilds2233]

One thing that is currently confusing me with this topic is why (e^(4x)(dy/dx)+4ye^(4x))=(d/dx)(ye^(4x)). every time i try to do it out myself i end up with it equaling (d/dx)(2y^(4x))

[@rollicconducto1550]

shouldn't the e^-(4x) be multiplied instead of added?

[@moonagedaydream1111]

Yep, good thing he multiplied it.

[@danielshin4515]

God bless your soul

[@ac-jk9mz]

You are the best

[@mhomo]

tysm for the 2 vids, 😀

[@thanatosdriver1938]

I don't know if anyone will read this but how could I have known that (e^4x)y'+(e^4x)4y is the equivalent to d/dx (e^4x)y? How was I supposed to come to the conclusion that it is. I know it works because of the product rule but that depends on me knowing the answer is (e^4x)y in the first place

[@scrub3359]

You can verify it be working backwards with the product rule. It might be easier to see if you regroup it like this: The term that made it click for me was *(e^4x)4y* --> (4e^4x)y f(x) = e^(4x) f'(x) = 4e^(4x) g(x) = y g'(x) = y' so you can rewriting as: f(x) * g'(x) + f'(x) * g'(x) which is the same form as the product rule

[@DerrickWasCracked]

Great video

[@dsizov]

Awesome, thanks a lot!

[@DrTrefor]

You're welcome!

[@saeedagha3127]

Thank you bro

[@CaptainSchlockler]

Why can't all maths professors be like this?

[@songhuang6854]

thank you so much, my professor isn't bad but I just forget and can't find my notes

[@AverageKopite]

Does anyone know what app he is using?

[@jobokal5930]

Good video but kindly use highly contrasting colours for visibility, the background is soo dark

[@steveying1305]

amazing video

[@skill7815]

please blink for the love of god

[@MariaDominguez-es8qj]

wouldn't it be c=-1 not c=1?

[@erms_234]

very nice

[@aleeyain192]

thanks boss

[@eigentheory]

A => would have been helpful on the solution to C line to disambiguate the equals chain. It was really confusing to many of my students. Something like this 4/3 = 1/3e^-(0) + Ce^(-4(0)) => 4/3 = 1/3 + C. I see this a lot actually, and I agree students should know these steps, but the students that didn't make A's-B's in lower classes may not all have this refined intuition.

[@8c04cheunglokhim9]

As a grade 9 student, I was able to comprehend that.

[@KyubiCloaks]

Why did 4y turn into just 4

[@chg691]

Nice...

[@DrTrefor]

Thank you!

[@AhmedAshraf-se4jj]

Dr please what is the best book of linear algebra if I want to learn more about it of course with your course🙂🙂

[@DrTrefor]

THis is an open source version: buzzard.ups.edu/

[@AhmedAshraf-se4jj]

Thank you dr and thank you for your time you are great at all 😀😀😀

[@continnum_radhe-radhe]

🔥🔥🔥

[@SHAHHUSSAIN]

♥️♥️

[@vinitdhandharia3478]

First : )

[@DrTrefor]

Nice one!!

[@vinitdhandharia3478]

@@DrTrefor Thank You Sir 😅, You are very inspirational. You teaching skill are really amazing ❤️

[@jayzieayangco912]

HINDI

[@burhan8795]

What happened to the Plus C in the integration factor