Session 7: Exact Differential Equations along with examples.(See pinned comment)

In this video, we will see what do we mean by the total derivative of a function. Then we will see what do we mean by the Exact differential equation along with some examples. Then we will see a theorem that gives the necessary and sufficient condition for a differential equation to be exact. At the end, we will see an example/algorithm to find the solution using the exactness method.

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Link for Variable separable method:

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Link for reduction to the variable separable method:

[DrMathaholic]

Everywhere I have said: " First-order Linear Differential equation". Actually, it is a "First-order Differential equation". Please ignore the word "Linear".

[simranmanghwani]

1) 2x^3 -xy+3x+y^3-2y=c
2) x^2y+cosx - siny=c
Really, your efforts are appreciable sir!!

[rohitpawar]

Thanks for this nice explanation, Sir! 😁

[maulirudrawar]

Nice sir. I understood the every concept sir.before this lecture I was so much confused why to take that k(y) as constant but now it's very clear. Thank you sir. And sir plz upload next units also.

[shahushinde]

1) 2*(x^3) - xy + 3x + y^3 -2y = c
2) (x^2)*y + cos(x) - sin(y)

[manavpatil]

very nice explained and canceling term by chalk was vey well

[omgawande]

HW 1)C = 2x^3 - yx+3x+y^3
HW 2)C=yx^2-siny+cosx

[shubhamkshirsagar]

2x^3 - yx + 3x + y^3 -2y = 😊
X^2y + cosx - siny = 😊

[vaishnavijasutkar]

Thank you so much sir for your efforts.🙏
1. U(x, y)=2(x^3)+3x-xy+y^3-2y
2. U(x, y)=(x^2)y+cosx-siny

[hubslearn]

Q1) 2x^3+y^3-xy+3x-2y=c
Q2) x^2y+cos(x)-sin(y)=c

[aakankshasonawane]

1.2x^3-xy+3x+y^3-2y=u
2.x^2y+cos(x)-sin(y)=u

[shreyamaggo]

Thank you very much for this lecture series, Sir. It is extremely helpful. Could you also prove the necessary and sufficient conditions in one of the upcoming lectures?

[sanmeetwakchaure]

Sir, I liked the way you cancelled the terms at 16:02😅
Very nice video sir...

[azadahmed]

Is there any website or some other thing which has this books solutions

[helloworld-hvoy]

where did u(x, y) come from suddenly ? at 8:13

[prafulkadam]

Is there exactness for second order or higher order differential equation

[azadahmed]

There is a simple formula for solution if equation is exact i.e
{M+{Terms of N not containing x

(Bracket are symbol of integration because my keyboard doesn't have)