Higher Order Constant Coefficient Differential Equations: y'''+y'=0 and y''''-3y'''+3y''-y'=0

In the previous videos in our ODE playlist we have seen how to solve constant coefficient homogeneous second order differential equations like y''+2y'+y=0. We saw how there were three options, distinct real roots, repeated real roots, and complex pairs to the characteristic aka auxiliary equation. The same basic idea applies for higher order differential equations as well, its just that we have more roots but they are all the same possibilities.

0:00 Intro
1:00 Example 1
6:40 Example 2

OTHER COURSE PLAYLISTS:

OTHER PLAYLISTS:
► Learning Math Series
►Cool Math Series:

BECOME A MEMBER:

MATH BOOKS & MERCH I LOVE:

SOCIALS:

[davidfarning]

Thanks for doing these videos. I am a self-taught roboticist. You have become my go-to channel for math. Whenever I come across something in my reading I don't understand, I go to your playlists and look for relevant topics. It is pretty common for me to watch a video a couple of times over a few days before I become comfortable relating the material to my work. If I am still struggling, I look for an OCW lecture. With the good foundation your material provides, even the stuff from MIT is reasonably understandable.

[chawnneal]

A small mistake at 5:17, the constants should be c1, c2, and c3.

Thanks so much for all of your playlists! They're really helpful for my self-studying!

[pipertripp]

Viewing these vids after some exposure to ODEs has been great. It's really nice to already have some context as it makes the inform stick a bit better the second (or third) time round.

[oliviab]

I've already taken Differential Equations but I love how you break down your explanations, so I watch for fun. Thanks for another great video!

[hdheuejhzbsnnaj]

These videos are neat, tidy, to the point, and clear. That's what we want! 👍

[lolnoventa]

I'm very new to differential equations and I swear your videos are by far the best explanations I've seen so far, thanks a lot!

[giraycimen]

If you were an instructor of my diff class, even if the class was at 8.am all of your coffes'd be from me. Thank you so much man i really appreciate your work and efforts.

[dominquepresley]

You're saving my butt right now. I'm a chemist that wants to be a chemical engineer.. engineering mathematics has been kicking my butt..

[utuberaj]

Very Nice and crisp explanation of how the basic idea of solving homogenous homogeous ODEs (with constant coeff) of orders>2 is SIMPLY an extension of finding the solution of ODE's of 2nd order.
I recall in college we learnt about the 'D' (differential) operator in the similar to the "r's" in "characteristic" equation.
I would request you to make a separate video on this 'D' operator (attributed to the genius American engineer/mathematician Oliver Heaviside), and its inverse '1/D' ( which is the integral operator) and use the Laplace Trasform and makes solving homogenous ODE's of any order look so simple- almost like school algebra and is a standard tool used to solve complex circuits in electrical engineering.
Looking forward to more gems from you Prof Bazett

[georgesadler]

Professor Bazett, thank you for an excellent video/lecture on Higher Order Constant Coefficient Differential Equations. DR. Bazett, when you factored r^3 +r equal to zero, you have r(r+i)(r -1)equal to zero) instead of r(r + i)(r - i) equal to zero. There is also two c2 in your final solution. Please correct these small errors in the video.

[iremiposiajayi]

Thank you so much for this easy and clear explanation!!

[evelyneakankwasa]

I liked this you have helped me understand these ODEs

[j.o.]

Is it supposed to be C3 and not C2 at 5:12?

[Darkev]

A mighty beard and a mighty video. Brilliant!

[marckymumvana]

Thank you for clear explanations what about for non homogeneous higher order differential equations

[ilias-]

Didn't expect to find better than khan academy

[PotassiumLover]

at the end, when finding the c4 term, instead of multiplying the c3 term by t, could you multiply the c1 term by t to get c4*t as your final term instead?

[MarisaEsau]

e to the it power is cos(t) + isin(t). you're supposed to add an i in front of the sin(t)

[sjn]

Nice video! Beyond pure mathematics, just curious what physical phenomenons can be modeled with higher ordered (>2) differential equations?

[devrimeskibina]

At 5.18, Should the third constant in the final answer be C3, instead of being equal to the second constant C2 ?