Math: Partial Differential Eqn. - Ch.1: Introduction (19 of 42) First Order PDE: Example 1

[@ahmedal-ebrashy3691]

Bless you heart Sir. That hasnt been easy to comprehend at all. Still spinning my head at many steps. Thank you so much

[@MichelvanBiezen]

Happy to help

[@PaulQuelet]

I didn’t understand the step of using an exact equation.

[@curtpiazza1688]

I think I' m getting it!😊

[@MichelvanBiezen]

You're welcome!

[@gevodem]

Do equations like this arise often in physics?

[@MichelvanBiezen]

These types of equations are not common in physics, but you need to be prepared to whatever may pop up when solving physics problems.

[@gevodem]

@@MichelvanBiezen absolutely. Thank you!

[@AL-kn4yx]

When we integrate x^4 shouldn't there also be a constant of integration C? Or does that become a part of the final integration function f(y) ?

[@bigbrothersinnerparty297]

There are no extra constants in an exact equation I believe.

[@leticiazarate9553]

Typing error in 5:22 😊

[@MichelvanBiezen]

Thank you. 🙂

[@Nutshell_Mathematica]

3.17 hope u mean x^m-1

[@MichelvanBiezen]

Yes the m should have been written a little higher.

[@arkyin3860]

Well ,im not the only one who doesnt understand this

[@MiguelFernandez-ix8mi]

How is m = 3? If you plug in m=3, you get 3x^2=x

[@nguyenkhoanam8930]

to be easier, m .B =3.B with B = 3X^(m-1), he wrote a little bit wrong line !

[@hepp00]

Yes you right ​@@nguyenkhoanam8930

[@turboleggy]

You lost me on this one. I dont understand what happened after the "TO BE EXACT" part either. Thanks you for going over first order my teacher completely skipped it and went to second order.

[@Winbugs1]

In order to understand what happened after the "TO BE EXACT" Part ,you need to see the "Exact Differential Equations". on the google or the lecture series of this teacher with the playlist of "Ordinary Differential Equations".

[@AliBarisa]

I think he should write: m(x^m-1)=3(x^m-1) thus, m=3 if you compare the two sides of this equation. That why, the integrating factor, F(x)=x^m=x^3

[@JenniferWhite-l6r]

Jackson Timothy Lee Amy Martin Kevin

[@wwoww520]

I'm sorry but it explained not well

[@TheJolgo]

This is a terrible notation abuse.

[@MichelvanBiezen]

What specific notation did not you not like?

[@TheJolgo]

@@MichelvanBiezen The notation you use is fine but you are abusing it. These are not frations. You can't multiply by dx. I know the solution is correct in the end but it's only a mnemotechnic, you don't explain this at all.

[@MichelvanBiezen]

That is how it is done in every math book I have ever seen. (and it is mathematically correct)

[@TheJolgo]

@@MichelvanBiezen Well if you've seen only very applied books then I believe you. It doesn't mean it's correct though.