I'm studying for my final right now, and since the lectures didn't make sense I came to youtube. I've been learning more by binging your videos than going over my dozens of pages of notes! Your videos are phenomenal, thank you!
I had to solve a very similar DE for homework and this video was very helpful. Loved the good vibes with wich you teach. Thank you for uploading this content and greetings from Argentina!
I just came across your ODE videos today. These help out a LOT more than my own online class videos! Thanks so much for making them. We're up to this material too. Not sure if you're using the same book by Nagle/Saff/Snider. Fundamentals of Differential Equations, 9th Edition.
@@TheMathSorcerer Cool. I wonder how many community colleges besides mine have ODE class. We have up to ODE, calc 3, linear algebra, and 2 discrete classes at mine.
Because you only have an m for every order of differentiation in the original equation. For the term 5*y, the original function is the zeroth derivative of y, so there is an implied m^0 on this term (which of course is 1). It's the first derivative that have an m in the characteristic equation, and the second derivatives that have m^2. Note: I'm accustomed to using r for this method, instead of m. Given the diffEQ y" - 5*y = 0 Assume the solution for y = e^(m*t) Take derivatives: y' = m*e^(m*t) y" = m^2*e^(m*t) Construct original diffEQ with the assumed solution: m^2*e^(m*t) - 5*e^(m*t) = 0 Factor out the e^(m*t): (m^2 - 5)*e^(m*t) = 0 Since e^(m*t) cannot be zero, we want the quadratic to be zero instead. Thus our characteristic equation is: m^2 - 5 = 0
I wish i had you as a teacher, I would of never missed a class because of how interactive and fun it must be. Thank you for the videos!
I'm studying for my final right now, and since the lectures didn't make sense I came to youtube. I've been learning more by binging your videos than going over my dozens of pages of notes! Your videos are phenomenal, thank you!
You are welcome!
this might be the first time ive actually yearned to see how the video ends. Super engaging! every math class needs a teacher like this.
this video is phenomenal, my current professor sucks at teaching. Get's me asking why there aren't more professors like you at Texas Tech University
can u teach me this
wow this was so much helpful than my tutors on campus. Best video I have learned!
Thanks sir, i love your teachings
I had to solve a very similar DE for homework and this video was very helpful. Loved the good vibes with wich you teach. Thank you for uploading this content and greetings from Argentina!
👍
I just came across your ODE videos today. These help out a LOT more than my own online class videos! Thanks so much for making them. We're up to this material too. Not sure if you're using the same book by Nagle/Saff/Snider. Fundamentals of Differential Equations, 9th Edition.
I used Zill to teach that class, BUT, I used Nagle/Saff/Snider when I took the class:) Very similar books!
@@TheMathSorcerer Cool. I wonder how many community colleges besides mine have ODE class. We have up to ODE, calc 3, linear algebra, and 2 discrete classes at mine.
"the big d just got absorbed" lmao
Thanks so much your efforts as been so helpful.
love this guy. Appreciate you help learning ! Thank you
Very helpful, thank you!!!!!!!
You are welcome😃
Interactive teacher
Dope teacher
Thanks sir
thankkk youuu
You are welcome!
Thank
you are welcome!
From y" ‐5y, why is it =m^2 +5 and not m^2+5m
Because you only have an m for every order of differentiation in the original equation. For the term 5*y, the original function is the zeroth derivative of y, so there is an implied m^0 on this term (which of course is 1). It's the first derivative that have an m in the characteristic equation, and the second derivatives that have m^2. Note: I'm accustomed to using r for this method, instead of m.
Given the diffEQ
y" - 5*y = 0
Assume the solution for y = e^(m*t)
Take derivatives:
y' = m*e^(m*t)
y" = m^2*e^(m*t)
Construct original diffEQ with the assumed solution:
m^2*e^(m*t) - 5*e^(m*t) = 0
Factor out the e^(m*t):
(m^2 - 5)*e^(m*t) = 0
Since e^(m*t) cannot be zero, we want the quadratic to be zero instead. Thus our characteristic equation is:
m^2 - 5 = 0
noisy
Thanks sir, i love your teachings