The Theory of Higher Order Differential Equations

Previously in my ODE Playlist we've talked about the theory of 1st order or 2nd order differential equations. Now we turn to the more general nth order ODE, specifically focusing on linear homogeneous ODEs. A lot of the theory is the same, but we have a few complications to deal with. Firstly, we have a new Existence and Uniqueness theorem for linear ODEs. Next, we have the principle of superposition which allows us to take linear combinations of solutions and deduce new solutions. Finally we describe the method to find the general solution to an nth order ODE and use the Wronskian to verify linear independence of the fundamental set of solutions:

0:00 Linear nth order ODEs
1:52 Existence & Uniqueness
3:20 Superposition
5:00 General Solution
7:02 The Method

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[Darkev]

The way you present complicated topics in such an elegant way is just brilliant! Why can’t you be my math professor QQ

[michaell]

Professor, you have my upmost appreciation, thanks to you who manage to teach me what my college professor couldn't under 10 minutes.

[BoZhaoengineering]

Fancy all math videos from Dr. Trefor. If you search math tutorial video, this channel is a must -see.

[georgesadler]

Professor Bazett, thank you for an awesome analysis on The Theory of Higher Order Differential Equations. Many topics in Differential Equations are similar to each other.

[imanfazel]

Fantastic! Very clear and concise. Exactly what I was looking for. Thanks!

[yarenkaya]

I am biased that I will grasp the topic that you explain where W[x] is not 0 (independent :)) of what the topic is.

[manrajmann]

just going to complete the playlist !
6 more

[PunmasterSTP]

Theory of higher order? More like "Terrific videos that are like no other!"

[ismailsevimli]

Thanks, I was totally lost with these topics till now :d. Do you think that we should be able to understand all this topics from a book quickly. Im asking because this same theorem is so hard to understand by reading it from a book. What is the difference, should we always watch videos to learn math?.

[Darkev]

May I ask what is the wronskian? Is this like checking whether a matrix has Full Rank or not (rank deficient) in the Linear Algebra world?

[sroydetroy]

Your videos should be getting way more likes but I mean WAY more likes.

[MuhammadInaamSufi]

I have a question can you define the algebraic structure behind this general nth order differential equation

[ankitkumarsingh]

Sir I have a doubt in propositional logic. If you can help me with a video then I would be grateful to you. The question is : how for all values of x implies there exist of x for particular P(x)?

[sherifahmedyehya]

Please Prof, Why while stating the general theorem, You defined F(x) = 0, Is it applicable only for the homogeneous ODEs ?

[sarafarahat]

When the solution of third order DE is y= c1 y1^2+c2 y2^2+c3?

[Ultiminati]

What if ith derivative of y((0) is equal to zero but the others are not equal to zero? There is no such b for that case, so uniqueness fails?

[suhailawm]

the number of bacteria on a plant follows a poisson distribution with parameter 60. find the probability of there being 55 to 75 bacteria on a plant

Gd afternoon professor. Plz let me explain that question. I got confused. (From Srilanka)

[yousefsaleh]

Your mic makes it annoying to hear you tho your explanation is incredibly good please s new mic

[LimaAlpha]

literally waxted my time and didnt understood a thing