Homogeneous Second Order Linear DE - Complex Roots Example

[Diproli]

Taddaa...we have our solution xD!

[Ghlan]

You, Sir, are the bomb.

[DDelacruz128]

patrick i have to thank you for helping me in 5 semesters of calc. 1,2,3 (2 was broken down to 2) and diff... it was all you. tomorrow i will take my last calc final ever and i feel ready thanks to you!

[jajapan08]

Mad respect foreal, your vids help me out a lot on my math problems.

[MHarlom]

Bro will you come lecture at my uni, you actually make maths fun!

[zeeshan3dge]

thanks a lot شكرا جزيلا

[LordRickIV]

I'd like to take a moment to thank you for these videos. Without them, I don't think I would have passed DiffEqs.

[Phacix]

hello, i have a question, how do you solve a "third-order linear ordinary differential equation?"

example:

y'''-4y''+7y' - 6y +0

[wpi2992]

thanks u've helped me thru calc 1-4 and now diff eqs

[wpi2992]

@wpi2992 oh and how do we send you money? i feel like i kinda def should since you've basically tutored me for a year....

[patrickJMT]

@wpi2992 you can visit my website (link is on my channel page), click on a link to any video, and there is a donation button off to the side. much obliged for any donations : )

[wpi2992]

@patrickJMT yeah no problem- like i said you've been great- i've gotten 2 A's and 2 B's in my 4 calc courses and i've been able to tutor my sis so $5 is pretty cheap thanks

[shadowC10ne]

Great video! Could you explain it to me why in certain book I'm reading the author chooses the constant values and reduces the solution even further? And also, how to do that? In one example he "chooses" 1/2 to be both constants in another a bit different.

[SuperPowderkeg]

This is a gr8 help Pa, thanx a million

[mattmc6]

Hi Patrick, I just wanted to let you know I failed Calc1 two times in a row, until I found your videos. I am now in my senior year of Engineering and got an A in every math class since. For that, I thank you.

[bobbyhoke]

so im trying to figure out a second order equation thats not in the same form...

y"(x)+1/3y'(x)=2/3 x y'(x)

[bobbyhoke]

so im trying to figure out a second order equation thats not in the same form...

y"(x)+1/3y'(x)=2/3 x y'(x)

[rubrbandball]

Thank you very much for these videos, they are so helpful. I can play guitar WHILE reviewing DE- it 's amazing. Also, I don't think enough people realize the implication of having someone like you willing to release these videos free of charge. It helps eliminate the pay-to-access "cram sites", including the stuff put out by the companies that already charge you $250 for their textbooks.

[Skone117]

why the fuck do i go to class? Why dont I just sit at home and watch this?

[shadowfrost91]

Is the quadratic formula inevitable, when dealing with Complex Roots? I'm not sure, but that's what it seems like (correct me if I'm wrong).

[rrazal1421]

isn't there supposed to be an 'i' next to c2?

ie y=e^(3x)(c1cos(2x)+ic2sin(2x))

[enjoyablesounds]

thanks a lot man.

[iquoez]

can i also get your videos on homogenous differential equations and non homogeneous diferential equation/ usingX=lamda+xandY=lamda+y all that stufff pleeeeeeeeeex help patrik

[iquoez]

i really am getting confused since i didnt get good teachers they just leave up the hard part as an assignment ? :(

[iquoez]

hey hi  these videos are awsm but can i get the idea that if we have a e^x+2y dy-e6y-2y dx then wat will be the solution i will be very thankful if u help me

[sujindanarak]

ขอบคุณหลายๆ ครับ

thailand thank

[patrickJMT]

@sujindanarak that is great : ) you are welcome

[mkberg05]

I Think I get it! Nvm Nvm! By the way go for the I <3 patrickJMT shirt! I need one of those.

[mkberg05]

How do you find the exact answer. For example you are given this same problem but y(0) =2 and y'(0) = 2. Getting the exact answer for the non complex roots makes sense but with complex roots it seems a lot harder. I can't find any thing that gives a good explanation on how to solve it.

[tessb]

the more i see other people's shit, the more i realize what a god you are

[patrickJMT]

@tessb ha - there is a lot of math stuff on youtube now. some is good, some... not so much (i think). glad you still like mine though

[omegadef]

Any chance you could do a video on solving systems of 2nd order Lin DE's?

I'm having issues.

[virdeesj]

Patrick!!! You Legend!!

[BronxBounty]

patrick you SUPERROCK!!!!!!! Thank you! ;)

[patrickJMT]

@BronxBounty ha, no problem

[armanika]

any videos on nonlinear diff eq's?

[patrickJMT]

@armanika i just bought some new d.e. books; i plan on making more of this stuff at some point. my day job is busy now though

[farshadguitar]

Thumbs up if you believe this guy & sal (khan academy) both deserve the NOBLE PRIZE !

[YostRS]

Thanks again!

[ppingpoong]

man... i learn so much from this than from my lectures

[b5thomas7]

I'm reviewing CALC 1-4 for a Navy interview and you've helped me a lot - Thanks

[patrickJMT]

@b5thomas7 my pleasure!

[speareon]

nice videos you have here! never thought differential equations can easily be solved like this. but, in your examples, you're only having coefficients as purely constants. do we apply the same thing for coefficients that are functions depending on x?

lastly, is (y')squared treated as a 2nd derivative of y with respect to x? haha. i'm just really confused. it's just a trick question that i can't quite figure out and hope you'll not see this one as a "homweork."

[ARMnonymosTASHNAG]

Patrick, you're my hero, you got my ass through first year!

now, a simple question what about the minus signs? in front of beta?

did i miss anything?

thanx bud

[ThMrksman]

You have no idea how helpful these videos are, good work!

[azizrezai]

Hey Pat, do u mind doing some videos on partial differential equations too. i know this is a bit of an open end request but i am soon going to be taking a class on it and just want to be prepared for it. if funding is required, i am willing to pitch in. thanks.

[DKF22]

omg u saved my asss, Thank you!!!! math is so fun when you know how to do it at least

[BolivianKing1]

Nvm I figured it out out ha

[BolivianKing1]

How is y'' + y' =0 solved?

[heady87]

@BolivianKing1

Alpha is 0 Beta is 1 , soln: y= c1*cosx+c2*sinx

[tmthomsen]

Fantastic.

[MICHAELMEMISBACL]

Can annihilator method be used by you? D^n where there is x^(n-1)

(D-a)^n where there is x^(n-1) and e^ax

[D^2 -2aD + (a^2 + B^2)]^n where there is x^(n-1), e^ax, and sin or cos of Bx.

[MrSilvia96]

good vid, cheers man

[SVBerk65]

yay pay $50k, skip class, and watch this guy!!!

[syaoranpies]

i love you

[Hatakek11223]

@syaoranpies JAME??? XD It's james. Do you really get this?

[marty4UOC]

hey, might be easier in an exam to 'complete the square', to solve the quadratic; to save time.

[okman1234567]

u and khan academy should collaborate into some sort of a monopoly youtube calculus site

[djkadirtube]

i'm super computer programmer.

[djkadirtube]

i love differantial equations. i love! i love! its for future. diff. is warranty of future systems.

[patrickJMT]

oh ok, hahahah!

actually, it is an old saying that no one uses anymore....

if someone says: yes, Virginia it is sort of like saying  yes, you idiot...

[amara01addis]

I never did enough maths modules at my 6th form college, despite the fact that i was always interested in pure maths. now that im a year older and in university, these videos are great to help me learn the stuff i missed quickly.

cheers!

[patrickJMT]

why would it be free in virginia?

and they have always been free to watch, so what is the problem? : )

help a brother out, i mean, c'mon....

[8888Duke8888]

lol

[garveya1]

I think he is confused by your profile description, I believe you were talking to someone named Virginia.

Not sure, that's what I gather.

[patrickJMT]

i took on summer class on C (one of only two people to get an A!)

and programmed using SAS will in grad school, but i have not programmed for many years.

so, i am certainly not a programmer, nor do i know/remember much about it.

[djkadirtube]

heey patric do you know indefinite integrating mathml input with c. i know c++ indefinite integrating algorithm. do you have a c/c++ class to upgrade code.

[ahboy89]

Hi, thanks for this great video it did clear some of my doubt. I'm just hoping that you could do a video of full homogeneous second order equation meaning with general solution & particular solution of complex root. Thanks!