Second order linear differential equation initial value problem , Sect 4.3 #21

Second order linear differential equation initial value problem , Sect 4.3 #21,
complex roots for characteristic equation,
complex roots for auxiliary equation,

blackpenredpen

[HeyrinAnnSonyBEE]

I love the way he smiles and sometimes laughs in between his explanation🤩

[reddheadedstranger]

I just had a lecture on this and your explanation made all the difference. Thank you so much for this.

[briankiptoo]

The clarity in your explanation is on another level. Thank you very much sir, may you live long to help us.

[theman]

Appreciate the lesson my man. Looking forward to more math videos for diffy q's :)

[mohammadzahidulislam]

what an absolute legend of a lifesaver

[aayushishukla]

Thanks sir for making this very helpful video.🙏

[fgjhnm]

Sr can we find initial conditions for a differential equation if these are not given?

[anthonyp]

You have saved me with this explanation!

[wiclifekimutai]

Really understanding but if I may ask Can't you use the other values i. e -1-1

[muhammadafzaal]

Thanks Sir.... I was searching this problem... And i got solution of initial value problem... Thankuu again Sir❤️

[mugiwara]

can you make a video on initial values for 3rd order differential equations, there will be 3 constants, how to solve those type

[zeerakasim]

You got my sub, thank you so much for making this video. Legit cleared my confusions loll.

[lucasvic]

Bruh, thanks. It is much better than my 50mins lecture

[grason]

It can use Laplace Transform (know y(0) and y'(0))
(s^2)*Y(s)-s*(y(0))-y'(0) +2[sY(s)-y(0)]+2Y(s)=0
(s^2+2s+2) Y(s)- 2s -5 =0
(s^2+2s+2) Y(s) =2s+5
Y(s)=(2s+5) /(s^2+2s+2) = 2s+5 /[(s+1)^2+1]
Y(s)=2 (s+1)/[(s+1)^2+1] + 3 /[(s+1)^2+1]

Inverse Laplace Transform
use 1st shifting Theorem
y(t)= L^(-1) {Y(s)} =2 e^(-t) cos(t) +3 e^(-t) sin(t)

[lawrencejohnson]

Mathematics teaches us that to every problem there must be a solution, thanks sir

[abhiramiabhi]

This lecture really helpful to me . Thank you sir...

[dipakkarki]

Thank u bro
Ur talking tone was quite unhealthy for me but I understood it
I had a simple mistake I forgot taking t=o😅

[michaelrainville]

Helpful lesson, really cute guy. 10/10 would recommend.

[DougCube]

You totally should have solved for 'r' using completing-the-square instead of the quadratic formula in this case. Would have been much cleaner. Trust your instincts :).

[Mehdi-qptz]

1:57 I don't get why y(t) is equal to that