🔵13 - Non Exact Differential Equations and Integrating Factors 1

In this video, we shall learn how to transform a non-exact differential equation to an exact differential equation and solve for the general solution.
A differential equation of the form M(x,y)dx + N(x,y)dy = 0 is said to be non-exact if and only if the partial derivative of My is not = the partial derivative of Nx;
thus if
My is not = Nx.
A non exact differential equation can be made exact by multiplying the D.E by an integrating factor u(x) or U(y).
Ones the D.E is multiplied by the integrating factor, the differential equation becomes exact and hence the general solution can be found.
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
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.
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Thank you.

[@reamabdulsalam524]

Ohhhh my God many thanks for this marvellous and helpful explanation I have spent two hours with my lecturer with no benefit of understanding any single word you are amazing

[@SkanCityAcademy_SirJohn]

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Thank you. Well explained and easy-to-understand video!

[@SkanCityAcademy_SirJohn]

Thanks so so much

[@mindrefreshment906]

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[@SkanCityAcademy_SirJohn]

Nice, that's great. Keep watching for more...

[@ryhan1422]

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May GOD bless you

[@SkanCityAcademy_SirJohn]

Amen, and thanks so much too

[@WarishBinKhurshidIndian]

Your lecture helpful for students

[@YoungGamingBoys]

Thank you so much! My lecture was useless and just skipped over this and it is very hard if you have no clue what this means. Blessings to you !

[@SkanCityAcademy_SirJohn]

Thanks so much

[@wmavila_14]

This is an excellent video. I was looking for straightforward and clear explanations on how to find integrating factors for non-exact equations and you delivered. Thank you so much.

[@SkanCityAcademy_SirJohn]

Aww you are most welcome.
Where do you watch from please?

[@wmavila_14]

@@SkanCityAcademy_SirJohn The U.S!

[@MUHAMMADARSLAN-m8y]

Extremely Thankful! Topic was well explained.

[@SkanCityAcademy_SirJohn]

You are most welcome. Keep watching for more

[@vince5127]

Best explanation so far, super easy to understand and you saved me a lot of time! :) thank you sooo much greetings from Austria

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[@SkanCityAcademy_SirJohn]

That's great, best wishes in your exams

[@SkanCityAcademy_SirJohn]

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[@vince5127]

@@SkanCityAcademy_SirJohn mechanical engineering

[@joshuanwokoye]

Thanks man

[@omeribrahim8863]

What happens if these two cases don't occur ?

[@nishadpsmechengg]

Thank you great videos

[@SkanCityAcademy_SirJohn]

you are most welcome

[@sarah-beth-thomson1034]

Fantastic explanation! Thank you!

[@SkanCityAcademy_SirJohn]

Most welcome

[@MoffatMkomba]

Mwatilowetsa muchimangatu

[@untitled_atlas]

how would you know whether to divide by N or by M, becasue in the explanation you divided by M but in the example you divided by N. Is it just intuition and hope it simplifies?

[@SkanCityAcademy_SirJohn]

You need to test for both, mine you.
If you get a function of X alone, case 1 is cool. If it turns out not to be so,
You test for case two.
So you need to check for case 1 and or for case 2

[@sandydosty7906]

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[@SkanCityAcademy_SirJohn]

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[@gloryjohn3200]

Well explained thatnk you❤

[@SkanCityAcademy_SirJohn]

You are most welcome

[@MawuliBen-j3f]

Hi Sir, please where can we access the textbook you use for your differential equation lectures? Want to try out more examples. Thank you. You are doing great

[@SkanCityAcademy_SirJohn]

You are most welcome
Download Allan Jeffery Linear Algebra and Ordinary Diff equ

[@abdurrahman-su4we]

Thank you so much sir🎉

[@SkanCityAcademy_SirJohn]

You are most welcome

[@atharvajambhale9729]

Hi sir , for ndx should be 0 cause x term is present in N as
N=2yx-¹

[@tikkashashank293]

x become 1 so answer will be 2y to the power of -1

[@atharvajambhale9729]

but the X is present in the Ndx term na ? And also replicates in the answer also .

[@atharvajambhale9729]

And we should be taking the terms in N which are totally free from X before any integration is done on Ndx?
This I wanted to say

[@danielasepulveda9143]

Thank you so much 🙇‍♀️🙇‍♀️

[@SkanCityAcademy_SirJohn]

You are most welcome

[@WarishBinKhurshidIndian]

I am from India

[@SkanCityAcademy_SirJohn]

That's great. Thanks for watching.
Which program do you read?

[@niyonkuruemile1036]

Wow this is very understandable 😍🥺💎 🇷🇼🇷🇼

[@SkanCityAcademy_SirJohn]

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[@SkanCityAcademy_SirJohn]

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thank you so much for this video

[@SkanCityAcademy_SirJohn]

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Very nice

[@SkanCityAcademy_SirJohn]

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[@adeyemiadedayo2001]

Thanks for sharing

[@SkanCityAcademy_SirJohn]

you are most welcome, and thanks for watching

[@manu-mm4pc]

Also what happin when both case are true? at 5:49

[@SkanCityAcademy_SirJohn]

just use one of them, in fact the one that can be simplified easily

[@nnamdiphilip9944]

What if it fails both cases?

[@SkanCityAcademy_SirJohn]

Then kindly check your calculation, else confirm if the D.e is of non-exact type

[@sayan-nj1mr]

I think you are doing partial differentiation of the m and n it’s confusing the way you have written?

[@SkanCityAcademy_SirJohn]

Really... Sorry about that. But please do you understand it?

[@sayan-nj1mr]

@@SkanCityAcademy_SirJohn yeah I understood sir I was confused by the partial derivative symbol in our university it’s something like inverted spiral

[@SkanCityAcademy_SirJohn]

@@sayan-nj1mr oh okay, thank God you understand it now

[@maricarmarzo6863]

Thank youuu!

[@SkanCityAcademy_SirJohn]

you are most welcome. keep watching for more and kindly suggest this playlist to your friends to watch as well ua-cam.com/play/PLInywrvFyvq408vWA5OYXShA6rlT51TdS.html

[@abeermelei9325]

Amazing thnx a lot 💕

[@SkanCityAcademy_SirJohn]

You are most welcome, Abeer

[@abdullahmirza249]

Case 2 solution please i am trying but I am unable to find pure function of y.

[@SkanCityAcademy_SirJohn]

Mmm what's the problem, where do you have the challenge

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[@SkanCityAcademy_SirJohn]

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[@SkanCityAcademy_SirJohn]

No please there is no shorter way. I took my time to explain so you can understand. But ones you do, solving other questions becomes relatively easier and consumes less time

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[@khuramkhalid5396]

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[@SkanCityAcademy_SirJohn]

you are most welcome