2nd order homogeneous linear differential equations with constant coefficients | Math with Janine

In this video tutorial, I demonstrate how to solve 2nd order homogeneous linear differential equations with constant coefficients. First, we need to write the auxiliary equation (aka the "characteristic equation"). After this, we can either factor or use the quadratic equation to solve for our roots. The nature of our roots determine the form of our general solution.

There are three possibilities:
Case 1: The discriminant (b^2-4ac) is less than zero ( real and distinct roots)
Case 2: The discriminant (b^2-4ac) is equal to zero (repeated real roots)
Case 3: The discriminant (b^2-4ac) is less than zero (conjugate complex roots)

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[clgniskoc]

Merhaba sizin sayenizde matematiği öğreniyorum yararlı videolarınız var hem zekisiniz hem de güzelsiniz ☺👍

[acentasecond]

Awesome video, definitely needed a refresher on this 😂

[mathew_pang]

Wow ! Great content ! good to see more and more passionate math teacher join YouTube 💪🏼 keep it up 👍🏼

[最後の浪人]

Thanks for making these tutorial videos! I'm always trying to find clear ways to better understand mathematical concepts (definitely not my best subject) and the way you break the problems down and explain them step by step is really helpful.

[colinalexandersledge]

Very clear explanation! It is always nice to see these complicated concepts broken down simply. Thank you for helping us! Can't wait to see what comes next! :)

[elephantdinosaur]

Whenever the clip gets fast forwarded or skips to a clean whiteboard with a new statement written at the top, I breathe a sigh of relief. Thanks for editing xD

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I don't understand everything you say, but you are really charming….