Second Order Linear Differential Equations

This Calculus 3 video tutorial provides a basic introduction into second order linear differential equations. It provides 3 cases that you need to be familiar with. It explains how to find the general solution of the differential equation as well as how to solve the initial value problem and the boundary value problem.

Lines & Planes - Intersection:

Angle Between Two Planes:

Distance Between Point and Plane:

Chain Rule - Partial Derivatives:

Implicit Partial Differentiation:

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Directional Derivatives:

Limits of Multivariable Functions:

Double Integrals:

Local Extrema & Critical Points:

Absolute Extrema - Max & Min:

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Lagrange Multipliers:

Triple Integrals:

2nd Order - Differential Equations:

Undetermined Coefficients:

Variation of Parameters:

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Final Exams and Video Playlists:

Full-Length Videos and Worksheets:

[AiZeno]

not gonna lie, this 25 mins video = 2 lecture classes of 2 hour = 4 hours of lecture and is paid. Whilst this is free. You deserve something better!

[thunderbolt]

dear school teachers stop skipping steps and start telling us both the how and why! like this guy in the video!!

[blakkermambaa]

You should be getting my tuition instead of my university. I've learned more physics, chemistry, and calculus from you these last few years than I have from most classes. Thanks!

[lasithathilakarathne]

This 25 minutes covered a two and a half lecture that I didn’t even understand...Thanks a lot♥️

[rmdir]

I appreciate how you dive quickly into actually solving problems, rather than getting bogged down in theory. At times the theory is important, but most of the time we just need to get straight down to business. In the long run, this no-nonsense format is more useful than any other math tutor on youtube.

[Jadester]

You are such a hero man. Seriously I can't think you enough, your generosity in sharing all this knowledge in such a compelling way genuinely makes me want to cry. You have helped me so much in my college classes, thank you.

[virajgorthi]

For Case 3, one tip my professor gave us was to solve by completing the square for the quadratic, then square rooting the function on both sides. It's a lot easier and gives you the same answer as the quadratic formula

[sijaladnani]

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[nahomfekadu]

It was very good tutorial but i have a doubt starting from example 2 which is like
y''-6y'+9=0
r^2-6y=0 not r^2-6y+9=0 (the question is given 9 not 9y but you're working the calculation as it were 9y.)
make a correction sir....

[jessnunn]

On questions 2, 3, should it not be in the form ay''+by'+cy? Instead of ay''+by'+c?

[lynnroach]

I love that these videos always explain each step, even stuff learned in previous math classes. I'm doing this in calc 2 right now, but I always get rusty on factoring polynomials when I haven't done it in a while, but whenever he explains it I feel like it all comes back. My professor would probably just say that we learned this in Int. Algebra which is true but we can't always remember everything off the top of our heads!

[baps]

5:07 - Case 1 Example
6:53 - Case 2 Example
8:45 - Case 2 Example
12:50 - Case 3 Example
16:28 - Case 3 Example (with initial values)
21:22 - Case 2 Example (with boundary values)

[Kgt]

This man has saved me countless hours by actually being able to teach the subject. Thank you so much

[HeyKevinYT]

Previous video: “fraction”
me: *presses upgrade*
This video: “SECOND-ORDER SEPERABLE DIFFERENTIAL EQUATION”
me: *GO BACK GO BACK!!*

[shivamrpatelofficial]

Your videos have saved me so much time especially a night before my exam. I have been watching you for years and I appreciate you for spreading the knowledge to all of us in such a simple way.

[vincentprado]

I was so confused. He made a few mistakes. To get a C, the term should have a y in it. It can't stand alone. Like for 9y''+24y'+16=0. In order to get the solution that he got, he actually solved 9y''+24y'+16y=0

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[kevincui]

We spent an entire week on this one topic at my university and I didn't learn crap, yet after this 25 minute video I just breezed through all the homework! Thank you!

[georgesadler]

Professor Organic Chemistry Tutor, thank you for an awesome video/lecture on Second Order Linear Differential Equations. Second Order Linear Differential Equations are simple to follow and understand provided that students have taken Calculus I and II. Thanks to the viewers for finding and correcting the error/errors in this video.

[ek_minute_]

People!! Did he just taught us solving differential equations in such an easy and beautiful way such that we're not going to forget it in this life??!