Same here man. I was just stuck thinking about them complicated notations used in the book. And I felt something clicking in my head, but lost it. Then I watch this video, and with a little bit of evaluation, I finally understood it.
Holy f***… been struggling with this for almost 2days now. At a point, i feel like i get it and then the next minute, it makes absolutely no sense💔… You just clarified everything in less than 3minutes. Thank you soo much🙏🏽
To get to F(x, y), there are 2 paths: 1) Take the integral of M(the x component) and adding the leftover component of f(y) 2) Take the integral of N(y component) and add f(x) Then, partial derivative of the variable side you did not integrate, which is equal to the opposite side. He took path 1 in the video: F(x, y) = integration(M)dx + f(y) [he used g here, but ill just call it f for simplicity] = x^2y^2 - 4x + f(y) Then, partial in respect to y of this = N: 2x^2y + f'(y) = 2x^2y + 3 [Shares same 2x^2y, so can cancel] Hence, f'(y) = 3 If you did path 2 you would've gotten the following: x^2y^2+3y+f(x) Partial in respect to x = M: 2xy^2+f'(x) = 2xy^2 - 4 f'(x) = -4 These both show up in the answer of x^2y^2+3y-4x = c This makes me wonder, since it seems that you could integrate both sides according to their respective variables and just add the shared portion with the non-shared portions. Edit: I noticed down below that another comment had the same exact idea, so this is a valid and at that, a speedier approach.
theres no way i clearly understood this concept in this less than 3 minute video as compared to me not understanding the college professor who gives an hour lecture on the same topic irl
It is a shame you get a book call differential equations for dummies and then you have to look on youtube for videos to explain the material in the book. At the beginning, why do you differentiate the function with respect to the opposite function to see if it is exact?
The reason I ask is because I saw problem in a book which if I did it correctly was with respect to the same variable in both terms, so If you try test exactness with respect to one x term and one y term, it was not exact and .you could not solve the equation.
I set it to 1.75 speed cause original speed was kinda slow. It's not too fast. And if it is for some; just set the speed slower. Or watch it multiple times. Or both.
Your process was way more complicated than it has to be. Take the integral with respect to X of the first equation and write C as C(y). Then take the integral with respect to Y of the second equation with its C written as C(x). Write them side by side and find all the matching terms, y only terms match with C(y) and x only terms match with C(x). Whatever is left set equal to C and you’re done. Why make it do difficult?
Because you’re mindlessly doing things without rhyme or reason and this way if you understand what you’re actually doing this way which is the way most books and classes teach it makes sense?
![Exact Equations [ODE]](http://i.ytimg.com/vi/pgJci5CI9n4/mqdefault.jpg)
I hate math but when someone explains it I love it. Thanks bro
Real
@@ahmeda.alnahrawy69
Damn 10 years later
Realllllllllllllllll
Oct 14
2024
u diggin
how amazing! he uploaded this video 9 years ago and it still helps us! Thank you Mr.
haha just wait until you hear this theory was there since 1680's
dude.. you just taught me this in 3 minutes. god bless America for having teachers like you
I am so glad this helped someone!!
I swear I never unlocked such big power in so little time. Thanks!!!
😂 the fact this taught me more than what my professor did in an 90 min lecture
nothing more nothing less, professional solution straight to the point good job helped me a lot thx
Math sorcerer, you're a LEGEND! Thank you for your service all these years.
This video made me learn more about exact equations than I learned in my past 4 hours of studying it. Thanks!!
Same here man. I was just stuck thinking about them complicated notations used in the book. And I felt something clicking in my head, but lost it. Then I watch this video, and with a little bit of evaluation, I finally understood it.
Life is hard
It’s harder when you’re an undergraduate math student
My exam is harder
@@ahmeda.alnahrawy69 You can do it, brother, I did it, and it was hard but I won indeed
Real
Ya but I am more harder
Thank you, in 2 minutes you answered all my questions!
Wow, you did what my instructor and brain couldn't do for the past 2 hours.
I'm doing chemistry major (biochemistry) and for some reasons I have to study differential equations completely
This was helpful thank you
Holy f***… been struggling with this for almost 2days now. At a point, i feel like i get it and then the next minute, it makes absolutely no sense💔… You just clarified everything in less than 3minutes. Thank you soo much🙏🏽
This is such a giant mess, and you explained it so well
I really like your simple solution, well done! thanks for letting us have the chance to listen it , sending positive vibes and love :)
love these short and clear explanations. THANK you
Sir you're a genius!
This was so simple to undertstand, thank you!
love love love how short it is, unlike some videos....
This is a gem, thanks!
Thankyouuuu! Answered all my questions in 2 mins
Cay you explain why you substituted 3 with g'(y)
Thats a simple algebra, 2x sq. Y cancels 2x sq. Y on other side and what remains is g'(y)=3
You compare with the initial dy equation
To get to F(x, y), there are 2 paths:
1) Take the integral of M(the x component) and adding the leftover component of f(y)
2) Take the integral of N(y component) and add f(x)
Then, partial derivative of the variable side you did not integrate, which is equal to the opposite side.
He took path 1 in the video:
F(x, y) = integration(M)dx + f(y) [he used g here, but ill just call it f for simplicity]
= x^2y^2 - 4x + f(y)
Then, partial in respect to y of this = N:
2x^2y + f'(y) = 2x^2y + 3 [Shares same 2x^2y, so can cancel]
Hence, f'(y) = 3
If you did path 2 you would've gotten the following:
x^2y^2+3y+f(x)
Partial in respect to x = M:
2xy^2+f'(x) = 2xy^2 - 4
f'(x) = -4
These both show up in the answer of x^2y^2+3y-4x = c
This makes me wonder, since it seems that you could integrate both sides according to their respective variables and just add the shared portion with the non-shared portions. Edit: I noticed down below that another comment had the same exact idea, so this is a valid and at that, a speedier approach.
Compare those 2 eqns
Why -4x , where x came from
amazing video super simple and great commentary thank you!
oh my god! this was the easiest way to understand this topic!!!
Very helpful. Thank you!
bro saved me the day before the exam
theres no way i clearly understood this concept in this less than 3 minute video as compared to me not understanding the college professor who gives an hour lecture on the same topic irl
Mmm......
Great explanation 👍🏾👏🏾
What would be the interval for this solution?
Genius , just in 2 mins😄
Thank you so, so much for this video.
Watching it on 7-11-2024.. 💪💪 helpful
Please why didn’t you differentiate -4x
i need to know that
Thanks😊
Can someone please explain why we use del y when the original equation has dx in it?
Thanks professor good example
It is a shame you get a book call differential equations for dummies and then you have to look on youtube for videos to explain the material in the book.
At the beginning, why do you differentiate the function with respect to the opposite function to see if it is exact?
That is the method for establishing exactness bro.
The reason I ask is because I saw problem in a book which if I did it correctly was with respect to the same variable in both terms, so If you try test exactness with respect to one x term and one y term, it was not exact and .you could not solve the equation.
@@the_eternal_student ooo,, i did not see it.
We could integrate both and equate too
good video dude thanks
Thank you!
wow amazing , keep going
thank you
life saver.
Heathcote Trail
Very helpful
Thanks
Why did 17 years old me chose a STEM major
Odessa Island
i wonder why g(y) is created. I thought you get C
Romaguera Circles
thank you soo much
This is awesome
thanks !
Hello the video is already cracked >
Sawayn Curve
Ziemann Alley
going wayyy too fast.. if someone is coming to this video its because they dont understand it and youre explaining it so quickly like i would
I set it to 1.75 speed cause original speed was kinda slow. It's not too fast. And if it is for some; just set the speed slower. Or watch it multiple times. Or both.
Your process was way more complicated than it has to be. Take the integral with respect to X of the first equation and write C as C(y). Then take the integral with respect to Y of the second equation with its C written as C(x).
Write them side by side and find all the matching terms, y only terms match with C(y) and x only terms match with C(x).
Whatever is left set equal to C and you’re done. Why make it do difficult?
Because you’re mindlessly doing things without rhyme or reason and this way if you understand what you’re actually doing this way which is the way most books and classes teach it makes sense?
This seems like more of a seasoned approach. I think it'll be easier to learn the video-way first, then find your way while doing problems.
❤
Thank you sooo much
Thanks