Differential Equations - 25 - 2nd Order - Repeated Roots

Deriving the general form solution to a Constant Coefficient, 2nd order, homogeneous, differential equation with Repeated Roots

[donaldey]

I am enjoying the series, because I can enjoy the mathematics and reasoning. With no pressure to remember are possible testing in the future. Like going to an art gallery and enjoying the art.

[SmitSolanki-sw]

Hey man love the way you explain DEs!! The most comprehensive and helpful explanation of the topic!! hope you are doing well.

[nicholasgindulis]

Hey man I'm sure you hear this all the time but you by far have the most helpful clear and understandable differential equation videos on youtube. Much appreciated, and if you aren't already you should look into being a professor!

[Generalth]

Yay! It's back!

I'm loving this series.

[flaviusclaudius]

This series is fantastic; I wish I had it in second year, because these are very clear worked examples that are explained throughout, including the reasoning behind each step.

[taslim]

thank you so much for every thing you have done. i dont what would i have been without it.

[uselessdiscussion]

Oh! So is this here kind of like, when you solve for y the first time, you didn't solve for "the whole thing" because assuming the solution of form e^rt wasn't enough, and that the second time around, you really end up with the full expression for the solution with both components, naturally? I love how that ends up that way (if I am understanding it correctly), because it was hard for me to reconcile before the idea that we had found half of it this way, and have to go back to find the other half - when really the other way is just finding the whole thing which yes includes the "other half". Kind of like, idk say a series expansion, sin(phi) is expanded to ~phi, which is part of, but not the whole thing, and if you want the whole thing, just do a more in-depth expansion in the first place, rather than "looking for the other terms" haha. Loving this!

[willyschirino]

Bro... you are the definition of awesome

[ottodvalishvili]

Thanks a lot man, you explain things very easily.

[JB-indj]

Would induction be used to generalize to the orders higher than 2? Because I know if you have 3 repeated roots it would include a third solution x^2e^(m_1*x)