Complex roots of the characteristic equations 2

[ninja2008physics]

THANKS!!!

[dportal2006]

dude thanks a lot.

[hurryupche]

LOL the progression, a tranformation of what?! wow sic!

[hurryupche]

Ahha thats awsome!

[Rizmaestro]

i have a major exam in 5 days and I am pretty much revising by looking at all your vids. It's helping so much!

[Tempestelterna]

@Rizmaestro ill be doing the same thing :D

[xScuzzleButtx]

What is the importance of complex roots?

[bob9630]

Quick question about the relationship between C3 and C4. Since C3=C1+C2 and C4=i(C1-C2), are the choices for C3 and C4 truly arbitrary, or does choosing one, affect the choice for the other?

[effortless35]

@bob9630 It doesn't. Fixing C3 doesn't restrict your possible choices for C4. Take any pair of C3,C4 and you'll get a particular solution of the differential equation.

To state it differently, for any complex numbers C3, C4 you can find complex number C1, C2 such that C3=C1+C2 and C4=i(C1-C2)

[giovanni9107]

Explaining this took my teacher about an hour and at the end no one (including myself) got it. This 10 min explanation I got it right away. Thank you, Sal.

[srenhope]

You are amazing!

[legolas791]

God sent you for us to pass our test!

[sssandeep619]

it in nice.....!!!

[zero3609]

You are awesome, i completely understood the material. Thank you :)

[jessiemanak]

This is barely even the prequel to the movement SAL... having this quality of material so easily accessible to the entire world instantaneously... you my friend have started a revolution. and that word is TOO OFTEN used loosely! lectures will be streamable soon for all universities.. and i can imagine a wall-e type scenario where kids just sit in pods from the moment they can respond to visual and auditory stimuli in the not-so distant future.. and some of u fools r critcizing pronunciation..LOL

[greenhulk87]

when should we solve for 'r' and when should we leave it in complex roots equation.. ?? i mean at 08:30, we could have solve 'r', but instead we write in in complex equation to sub into other equation..

[lkkoller]

Euler is pronounced "oiler". I learned more in 3 days of your videos than an entire semester of Diff Eq! Thank you!!

[kailiong09]

Dear Sir !

Salute~ ｛＾＿＾｝

You're so great~

Thank you very much !!!

[wildrider100]

if u read this put a thumbs up for a good comment, and khan academy rocks!!!!!! :)

from dubai

[KSKTatti]

This is the best explanation that I have ever seen on this problem, may it be in a textbook or lecture or whatever. Sal, you rock!

[socialanthro]

You are AMAZING!!!!!

[ReaperUnreal]

Forgot to close a bracket at the end there. Great stuff though!

[demisous]

pleaaaaaaase answer me,,, is this the same as the d.operator method???,,, and what is the variation of parameters method ??????/ pleaaaaaaaaase people!!!!

[QbanoPuraSepa]

Variation of parameters method is the method that you use when ther are no constant coefficients. The formula is y2(integral)y1f/W+y1(integral)­y2f/W, where "W" is the Wronskian, "f" is the non constant coefficient on the right of the = sign, and "y1,y2" are the general solutions of the of the homogeneous differential equation....holla @ me...

[QbanoPuraSepa]

You may use the constant coefficients method if you had for example y''+4y'+4y=4x+cos2x+sin2x; where the form of a particular solution would be Ax+Bcos2x+Csin2x.

In order to use Variation of Parameters, on the right side of the = sign you may have "=4x+(e^2x)/2," for 4x you may still use constant coefficients, but (e^2x)/2 is not constant thus you would use the previous formula that I gave you, where y1 would =e^-2x and y2=xe^-2x, the W would come out to be e^-4x and your "f" would be (e^2x)/2

[MrThePresent]

dude... i love you...im not scared to admit it... true love right here

[weso353518]

thank u very much. appreciate it :D u r realy a great teacher

[tcmzueck]

Really, who comes up with this stuff? WHO FIRST THOUGHT TO DO THIS???

[cwxzeng]

very clear, thx

[misholk]

You're great!

Thanks

[nicoeatsnow]

Thx thats clear.

[BKproduction1906]

you rock the math man XD thank you

[m83ms]

i have a maths exam in about 5 and a half hours, and I cannot describe how much this is helping my last minute revision. thanks a buhunch!

also, i find it hilarious to try and follow the mouse on the screen with my own mouse.

try it and tell me you can do it without smiling! mind you, all the red bull i've had might explain my giddiness.

thanks again!

[ramirent]

Hey, passed? Mine goes in about 6 hours (next morning) :D

[PoleReseal]

nice video, thank you sal.

[janusanus]

when breaking a sum across multiple lines, i write a + sign both at the end of the first line and the beginning of the next line

[ivy0213]

you are so good!!

thx!

[irok]

i love you

[1corex1]

Ouch diffluct math

[roflmaofunny]

I LOVE YOU!!!thank you thank you!

[as8167]

U R a good teacher. Thx