🔵12 - Exact Differential Equations (Solving Exact Differential Equations)

In this video, we shall study Exact differential Equations and solve two examples.
A differential equation of the form M(x,y)dx + N(x,y)dy = 0 is said to be exact if and only if the partial derivative of My = the partial derivative of Nx;
thus if
My = Nx.
A differential equation of the form M(x,y)dx + N(x,y)dy = 0 is said to be exact if there exist a potential function f(x,y) such that;
df(x,y) = M(x,y)dx + N(x,y)dy........(1)
since df(x,y) is a function of two variables, its derivative is given by
df(x,y) = (Of/Ox)dx + (Of/Oy)dy..........(2),
hence:
M(x,y) = (Of/Ox) and N(x,y) = (Of/Oy)
Given a differential equation, the first thing to do is to test for exactness. If the differential equation is exact, then you move on to solve to find the general solution to the exact differential equation.
The solution of an exact differential equation must be of the form; f(x,y) = c, where c is a constant.
In this lesson we shall solve two major examples
00:00 - Exact D.E
03:02 - Ex 1
10:58 - Ex 2
Playlists on various Course
1. Applied Electricity
• APPLIED ELECTRICITY
2. Linear Algebra / Math 151
• LINEAR ALGEBRA
3. Basic Mechanics
• BASIC MECHANICS / STATICS
4. Calculus with Analysis / Calculus 1 / Math 152
• CALCULUS WITH ANALYSIS...
5. Differential Equations / Math 251
• DIFFERENTIAL EQUATIONS
6. Electric Circuit Theory / Circuit Design
• ELECTRIC CIRCUIT THEOR...
Make sure to watch till the end.
Like, share, and subscribe.
Thank you.

[@Only1retro]

nah ,ive watched all the videos on differential ,this is straight to the point, the best

[@Only1retro]

i can now teach someone,

[@SkanCityAcademy_SirJohn]

Nice....

[@SkanCityAcademy_SirJohn]

Thanks so much.

[@reamabdulsalam524]

Really I don’t know how should I thank you , you are the best tutor ever please do post more videos , you make my life easier I felt that I can’t solve the exact equations and started to get depressed by checking other tutors videos , but once I see yours ohhhh my god too easy , others make it too difficult!!!!

[@SkanCityAcademy_SirJohn]

Awww thanks so much for your comments

[@al-washisarkerturan8913]

The best video on youtube on exact D.E.You have literally saved my final.TYSM.
Suggestion : Using a black background would be better for those who need subtitiles.

[@SkanCityAcademy_SirJohn]

Thanks so so much🎉🎈, and suggestions well noted....

[@sulaymaneabdulqudus9367]

I have been searching for exact differential videos on CZcams and all I found was not explaining enough. But your video actually explained it to me more than I expected.
Thank you very much

[@SkanCityAcademy_SirJohn]

You are most welcome

[@Yeno__429]

And my lecturer was confusing the whole class with nonsense.. I can't thank you enough dude 🎉🎉

[@SkanCityAcademy_SirJohn]

thanks so much

[@gracepeterson1556]

Watching this literally 20 minutes before I go to take my exam and it finally makes sense...lol thank you!!

[@SkanCityAcademy_SirJohn]

Good luck Grace.where are you watching from?

[@narcissekabongo2616]

bro is saving my midterm🫡🫡🫡🫡🫡

[@SkanCityAcademy_SirJohn]

Thanks so so much and best wishes
Where do you watch from?

[@lekissdarams7195]

Thanks bro! Even a kindergartner will understand 🙌

[@SkanCityAcademy_SirJohn]

Awww. thank you very much.
Please where do you watch me from?

[@mensahbenjaminrabby3303]

Good video, simple and easy.
But please i also thought of that same question @Felicty asked. I don't have any example though but I will like to see conclusion on that when anyone finds out.

[@SkanCityAcademy_SirJohn]

Okay. Will let you know when she responds finally

[@thabisomaphopha]

straight to the point .😇 thank you

[@SkanCityAcademy_SirJohn]

You are most welcome

[@chairmanosa2304]

Thank you very much for the video, but i will like to ask, incase you are merging, and you find your answer in both Mx and Ny but with different operational signs how will u go about that.

[@SkanCityAcademy_SirJohn]

its very rare for such situation to occur, anyways if you have a question like that you can bring it up so i try at my end

[@hesedcharis4966]

This is lucid, Sir.

[@SkanCityAcademy_SirJohn]

Thanks so much

[@nyarkofelicityserwaa3031]

Please I used this approach to solve a question but I want to know in a situation where the coefficients of the common function are not the same how do you go about it? ie when merging integrals of Mx and Ny.

[@SkanCityAcademy_SirJohn]

If you have a typical question kindly send it to me.

[@nyarkofelicityserwaa3031]

So should I add the coefficients or just take one function ?

[@SkanCityAcademy_SirJohn]

You know it's rare to get such situations, so I just want you to send me the problem then I confirm at my end

[@lonlee9426]

Please which book did you get the questions from?🥺

[@SkanCityAcademy_SirJohn]

Schaums outline of DE

[@SirBen_1]

You gained a follower for this video ✅️

[@SkanCityAcademy_SirJohn]

Thanks so much

[@johncholmach7790]

Awesome video 👏👏

[@SkanCityAcademy_SirJohn]

@johncholmach7790 thanks so so much

[@abduljaleelsadiuba6717]

Beautiful tutoring

[@SkanCityAcademy_SirJohn]

Thanks so much Sadi

[@sesemunasia8681]

Thank you. Followed.

[@SkanCityAcademy_SirJohn]

You are most welcome

[@hensleysapom3525]

Okay, question here. Why to merge the two functions and write each only once?

[@SkanCityAcademy_SirJohn]

Yes that is a rule we need to just follow when solving exact d.e's

[@hensleysapom3525]

Okay sir. That's a very short way than the one in my lecture. Thanks, anyway.

[@user-gf3pg4pq6r]

❤thank you so much

[@SkanCityAcademy_SirJohn]

You are most welcome Rachel.
Where do you watch from?

[@abktv1054]

great man

[@SkanCityAcademy_SirJohn]

Thank you so much

[@GiftJordawe-gz1xr]

Thank you 👍

[@SkanCityAcademy_SirJohn]

You are welcome

[@MemorizeQuranEasy]

Bro thanks 👍

[@SkanCityAcademy_SirJohn]

You are welcome

[@engsmyle]

Sir if the exact is in this form
M(x, y) dx - N(x, y) dy = 0
can the solution be
dϕ(x, y) = ∫ M(x, y) dx - ∫ N(x, y) dy

[@engsmyle]

Sir am I correct, I just think of it

[@SkanCityAcademy_SirJohn]

I've not tested that, to be on the safe side, make sure you put the d.e in the form M(x, y)dx + N(x, y)dy = 0. Do you understand?

[@engsmyle]

@@SkanCityAcademy_SirJohn okay sir ❤️

[@engsmyle]

@@SkanCityAcademy_SirJohn sir I would like to send a question 🙂

[@SkanCityAcademy_SirJohn]

Thank you

[@oyedokun]

Determine the most general function M and N such that the equations M(x,y)dx + (2xy³-x⁴y)dy is exact.