❖ Exact Differential Equations ❖
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- Опубликовано: 28 янв 2025
- 📚 Exact Differential Equations: What They Are and How to Solve Them 🧮
In this video, I explain what it means for a differential equation to be exact and walk you through solving an example step-by-step. We begin by checking if the differential equation meets the necessary criteria, and then use partial derivatives and integration to find the solution.
🚀 What you’ll learn:
How to identify an exact differential equation.
The process of using partial derivatives to test for exactness.
How to integrate and solve the equation once it’s verified as exact.
Exact differential equations are significant because they represent a special type of differential equation that can be directly integrated to find the solution. This makes them particularly useful for solving real-world problems in fields such as physics and engineering, where systems are often described by functions whose differentials are exact, meaning they are path-independent, which simplifies the analysis of state variables and their interactions.
Key concepts of exact differential equations:
Direct integration: Unlike other types of differential equations, exact ones can be solved by straightforward integration since the differential is "exact" or "total," representing the total change of a function, regardless of the path taken.
State functions in thermodynamics: In thermodynamics, exact differentials are closely related to state functions, which depend solely on the system's current state and not the path used to reach that state.
Applications across fields: Exact differential equations are applied in various areas such as fluid mechanics, electrical circuits, and chemical reactions, where the system is often represented by a potential function.
Testing for exactness: To confirm that a differential equation is exact, we check if a specific condition involving the partial derivatives of the equation's coefficients holds true.
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Watch now to master exact differential equations and apply them to solve real-world problems!
#ExactDifferentialEquations #DifferentialEquations #MathTutorial #PartialDerivatives #Calculus #Mathematics #STEM #MathHelp #EngineeringMath #Physics #StateFunctions #Integration #EducationalContent
![Exact Equations [ODE]](http://i.ytimg.com/vi/pgJci5CI9n4/mqdefault.jpg)
![Exact Equations [ODE]](/img/tr.png)
Hi all! Wanna help a RUclips education OG? Please post comments, questions and anything else on your mind in the comment section! so, don’t forget to LIKE, THUMBS UP, and SUBSCRIBE! I’d appreciate it greatly as it helps me :)
You are a game changer in my math journey. I couldn’t have performed that well without you. Bring a mom and a student is difficult but your explanation makes everything easier to understand for me. Stay strong and blessed
@Zadamanim that is just how i want it.
i tutored two girls for about a year before they realized they had been watching my videos. : )
one day, one of the girls was like: you sound just like this guy on the internet whose videos i watch. you even have the same name...
1.5 hours worth of lecture summarized in 6 minutes.
Simoni Dulanto gotta put that fluff in to sell those text books 💰 💵
Hey. Did you pass?
the lives you have saved are endless
thank you
Agree.👍💯
Clear as water and so much faster than Khan Academy.
Glad I could help!
+Samir Fersobe haha Khan really confused me too. Pat explained eveything withing five mins.
+patrickJMT You got me through college math dude. Youre the bomb
+mamu7mich I too came here after getting confused because of khan academy😭
Samir Fersobe o
Been with you since my calc days im in diff eq and you have yet to fail me
jmt - stay with me 4evers lol
+genex i will always be in your heart
Thank you so so much @PatrickJMT I been watching your videos since I start college.
You saved me in PreCal, Cal 1 and Cal 2 and now in Differential Equations. God Bless you for every man.
you are the reason i passed calc 1, calc 2 and will be the reason i pass diff equations. you deserve a nobel prize i swear because however you are the reason every one in my uni passed their math courses. thank you so much
It's amazing how you can explain in 5 minutes something I spent a week trying to understand. Thanks!!!
I can relate. Thanks Patrick
I love it when he said "it will simply go away" 3:20
Shout out my nigga PatJMT been saving my ass since Calc1
Tony Tone saved me since trig
+Tony Tone for real. i want to shake this man's hand.
Tony Tone just too late for me
wish i had knowen him before
Just five minutes to completely explain a thing that I've been struggling to understand from my lecture notes for the past 20 minutes.
Great thanks!
you posted this video when i was 5…now i’m using it 15 years later…thank you so much for making the topic so clear!
Videos like this one are what really... DIFFERENTIATE... Patrick from other math tutors.
good pun.
@@sahilagarwal7752 Drumroll...
good comment
it's funny cause this exact problem was on khan academy
i USED to teach. teaching to me is always rewarding. but it is impossible for me to say what will be rewarding to you. it also depends on what sort of institution you teach at. i also taught at a community college for a while and it got to where i could not tolerate it. that is just me though.
Hi patrik I am not complaining at all you are amazing but please explain why you have chosen fx dx not fly dy for example
For anybody wondering like I was: the reason the exactness test works is because in an exact equation, M is the partial derivative with respect to x of F, and N is the partial derivative with respect to y of F. By the properties of symmetry of second partial derivatives, the partial derivative of M with respect to y should be the same as the partial derivative of N with respect to X, because F_xy = F_yx (this is a Cal 3 concept, and I'm taking Cal 3 and DEQ at the same time for maximum suffering, so I hadn't learned this yet)
@phanelius happy i could help : ) thanks for telling your friends, it is appreciated!
You're our saviour. Gosh, I did not even understand what my professor taught us for an hour and half but you did it in less than 10 minutes.
Almost 12 years later and still saving lives. kudos to you bruh.
thanks!
Patrick your tutorials are awesome, i will make sure to include your name in my degree certificate :)
I should be paying you, not Iowa State, for my diff. eq. class, and my taxes should be funding your salary, not my professor who makes 90 grand per and is... lets just say (as politely as possible) inefficient. I literally would not have made it through the first 2 weeks without your videos.
taking 267 rn and same
Truer words have never been spoken.
The only video out there ACTUALLY explaining the correct way to solve such questions. Kudos man! U made my day❤️❤️❤️❤️❤️❤️❤️
The use of colour helps a lot! You explained in 2 minutes what I my professor couldn't convey in 30-60 minutes. Thanks! Now I just need to re-watch this video once a day until I get a better grasp of what to do in chronological order. It's still hard to know whether to differentiate, or to integrate.
glad i could help you out a bit. best of luck in your studies!
@patrickJMT I was going through Khan's tutorial for exact equation. But after I found your's, it really helped me where I got stuck with Khan's. You are really gr8. you also deserve every penny because you are damn good in what you do.
Just wanna thank you Patrick, I’ve been using your videos since calc 1, now I’m in calc 3 and DE
happy i could help :)
Finally someone showing this method in a way that isn't confusing. The formal explanation is great for conceptual knowledge, but it complicates the process.
I have recommended you many times to my friends, I guess why professors aren't called teachers is because they cant teach! You are a saint in the world of mathematics, possibly a god.
After wasting more than an hour trying to understand the process from (A first course in differential equations book) with no success at all .. i can now solve most problems easily :)
Thanks a lot.
Your teaching is clear and awesome. I learnt from you more than all my maths lecturer. Thank you so much!!!
Its simple and clear, Thanks my best teacher for calculus.
2019 and patrickJMT is still the best...
Hi Patrick I'm watching you from Turkey and I want to thank you for your videos! When I don't understand the topic in the class I'm thinking directly about you and say "teacher Patrick will help me out" :) You are awesome !!
hey man, i love you! my lecturer goes so fast and I couldn't keep up! your videos made me very clear of the basic concepts :)
Patrick, you rock man. I have an exam in about 5 hours and just learned this in about 15 minutes thanks to your video.
God bless this whole series. I have a hard time focusing in class and these videos are the only way I'm getting through Calc IV
Been with your PatrickJMT since Trig. and here I am in my differential Equation, Taking my prefinals exam. Thank you for everything love from philippines
so happy i could help you for so long :)
You know, I could spend ten minutes reading a book and not get it, but watching your video for just seconds made everything clear. Good job! You're a concise and effective speaker.
Every time I am forced to take an advanced math class I just love you and your fantastic tutorial videos all over again. Thank you! :D
taking my last math final for Civil Engineering (Differential Equations/Linear Algebra) and I can't thank you enough!
Best maths teacher ever! Helped my pull my grade up in a exam by a massive margin as I did bad in coursework's but revised for my exam from your videos and got 95% but my bad coursework's pulled it down :(
I spent half a day trying to understand this on my own.
God bless u.
First I listen to the teacher and I understand it 50%. After that I listen to you and I understand 100%. Thanks a lot for these videos.
No fan fare or fluff, precise, to the point, very clear in the presentation. In short, an excellent piece of work.
Thanks for posting this and I'll be checking out the rest of your videos and website as well.
Five Stars.
Thank you for this video and you give a very clear explaination. I just watch this videos an hour before my final examination and it is really helpful for me to understand more.
Much easier than my prof! I've been wasting the entire day for some nonsense until I find this! Thank you!!
TL Alicetears yo u got instagram cause i need help with this ?
Appreciate the help, do not normally comment on these sort of videos, however, this was an amazing explanation!
I was doing this along with you and just realised, not only are the videos amazing, We use the same markers.
A 2008 video still saving lives in 2021 , lol. Thank you Patrick
Thank you soooo much. I have been struggling with this for a good week now, but this video made the "light bulb turn on." Fantastic video.
Now I understand the notes I took in class! Everything was just a jumble of M and N and x and y until I watched this. Thanks!
Patrick saving generations of college students, you're the best, thanks for everything and I wish you all the best.
happy to help! :)
hey man, this was a life saver - I couldn't figure out my textbook's mathelese, and this was incredibly helpful. thank you! one day, I hope you make heaps of money from helping kids like me.
I learned some engineering mathematics lessons from your videos, thank you a lot. Those videos are very well, we can understand easily. Thank You !!!
I have a calculus exam tomorrow and you helped me so much, So thank you a lot. I can never forget this (Y)
Many of Patrick's videos are around 10 years old but succeed in helping me every time
Than you so much!, You have been helping me since precalculus.
Thanks a lot. your videos is very helpful. I always watch your videos when i have a quiz or exams because you explain very well than my professors :D
I'm a third year university math student. I wouldn't even be able to pass high school calc courses without your videos.
glad i could help a bit :)
i think u r just the best math teacher in the world ...thank u so much
Good video....... this is the first time Im coming accross this type of differential equation and you just explained it amazingly... cheers
It's so simple and very clear explanation. Thank you so much! I finally understand my report in differential equation! You're my savior! :))))
I've been watching your videos since high school, I just started my masters and still watch 'em. Hope your doing well.
I hope youtube rewards these people. Imagine how many lives they saved? They can easily make a reward for those who have a millions of subsrciber. So why not this one?
thank you for the help! you taught me more in a half hour watching the differential videos than in class
Outstanding! Done in 1/3 the the time of another post and it's clearer.
Where would I be without you, PatrickJMT?
Thanks!
@martmelee any calculus book has them, usually at the end. you could probably just google it as well
great, i missed class today and have a quiz tomorrow, you just saved my life for this section! hooray!
@garnacov ha, happy to help : )
Thank you Patrick! Your method is so much better than my professor is school.
I missed a lecture so I'm having to watch this video about 5 times over to hammer down the process. Thank you!
Ah, so after watching this video for like 5 times I think I finally understand how to solve an exact equation now! lol. Thank you very much!
Im still pushing through my stem math classes because of you!
Sir You Save My Life , Cause i can't understand this topic, when i read my text book, and i such many videos but it's not to help me . When I saw your Video(class) , I'm just shocked 😧. It's Too easy......
Best wishes Sir ❤
Best playlist on differential equations
Anyone?
Patrick oh Patrick my Calc legend ! since calc 1 up to diff eq , you are really a life saver Oo
My ass got blisters from all the time you have saved me.
please make another example of these. and by the way, thank you so much for these videos, they have really helped me.
This was simple, straight forward and very helpful. Thank you.
Thanks a lot. This makes me understand a lot better than my lecturer do, even though English is not my native language.
Thanks for teaching! Now I could solve exact DE. This solution is clear and simple.
Dude... you explain in 5 minutes what my proffessor can't in a semester, I swear...
Exactly- in theory you add a constant of integration every single time you integrate but in practice as you say it all gets wrapped up in the fact that we are solving an initial value problem F(x,y) = C, so we can 'lump it all in' to the constant C
Mr. PATRICK you are going straight to heaven.
thanks sir , this is exactly the same example that my teacher solved in the class.. i couldnt ask more from you
THanks a million times.
This helped me both on my homework and final...
Keep up the good work
awesome as always Patrick keep up the good work
Thank you very much. I couldn't understand enough university math lecture. I can understand exact diffrentail equation now thank you
you are really good, thanks for this videos, they are really helpful for me in all my exams, etc. I like your style :)
You are the one,you always have a way of making me love math,thanks 😊
Thank you so much
greetings from Cairo - Egypt ;)
Thanks a lot for making these videos. I couldn't figure out what I was doing wrong until I watched this.
Oh my god. Thank you.
from this one vid i've seen, you already make up for me not having the textbook and a lousy Prof
thanks!! this cleared so much confusion during my lecture
great! come back any time
somebody gives this guy an oscar for best teacher!
Thanks a lot!!!!!!!!!!!!!!!!!!!!
May your Channel progress leaps and bounds!!!!
I solved my assignment question!!!!!!!!!
Great!
You did a Great job. Thanks for the help with this concept
You are so much better at explaining this than my textbook :)