2nd Order Linear Homogeneous Differential Equations 4

[unfreez]

This is just A level math, nothing fancy

[Oesquartejador]

r=-1/2 not r=1/2

[opjjuly]

isn't b = -8 ? why did you leave the -ve sign when substituting the values into the quadratic equation?

[opjjuly]

@opjjuly ohh im silly, got it. :-)

[l0lsammy]

Do you have a video for when the equation is equal to an exponential?

[bezzer1185]

Sal my man it IS a trivial one to factor (2x-1)(2x-3). its all good you are my hero! if i ever get extra monies its goin to khan academy!

[raj62846]

sir, im appering iit jam xam from chemistry ,n i want little help from you ,my exam is on 8 th of may ,plz help in studing more in small time

plz rpl im gvng u my email id nehavishwakarma20@yahoo.com plz rpl..................

[Constantine769]

Just figured what book you're using =). And the book's explanation is nowhere near to how clearly you are explaining it. Your videos are worth way more than what I payed for this badly written book.

I wish you were my professor for every math class I have. =/

[kewlgeko]

at 6:25, why wouldn't you multiply the equation by (-3/2)???? In Part 3 when you introduced this, you ADDED the two equations to cancel them, while this you are SUBTRACTING, does it matter then which operation you do??

In addition, is e^rx gonna be what's used for all of those equations? I remember you saying earlier, it was something u chose, but is that just the easiest?

[jastrott]

@kewlgeko

my attempt to answer your questions: in response to your first question, you very well could multiply the equation by (-3/2) and then ADD them. think way back to algebra. you have a set of solutions here, so you could do several different operations as long as its taking you towards singling out one variable. in this particular case, C1 or C2. so, no, it does not matter which operation you choose to do. choose whichever one you are most comfortable with!

[jastrott]

@kewlgeko

since you posted this a week ago, i'm sure you've had a chance to look ahead and see more diff. eqs., but just in case, you CAN and WILL use different equations to solve other types of second order linear homogeneous eq'ns. a good example is a second order Euler function. in that instance it is best to solve by letting y(x)=x^r. don't get too caught up with this, just keep watching the videos and start associating different equations (such as y(x)=e^rx and y(x)=x^r) with different

[jastrott]

@kewlgeko

diff. eq'ns. pattern recognition is your friend!

[gvalchca]

I'm taking this at 1st semester of electronics course. today I'm having an oral exam. fingers crossed ;)

Poland watches khanacademy :)

thx for your help!

[achintyagopal1486]

do you have videos on second order linear NONhomogenous differential equations?

[varvijviju]

y"-c(1+be^(a(Xf-X))y=0

With initial and boundary conditions.

y=P(x)

dp/dx = 0 @ X=Xf

P=Pw @ X = 0

c= u/(Kfhw)

Need final solution in the form of P(x)

Thanks much

[Rastaman12122020]

lol when i saw u add that 3r, it was like I was watching a movie and u went down the wrong hallway, i was yelling at the screen lol. ur helping me a lot btw

[tchoe074]

thank u very much....u saved my life...

[reicher89]

You are absolutely amazing. You give me hope in my differential equations class. thank you so much.

[iEatFanboys4Lunch]

idk y PHD profs have so much trouble teaching this shit

[gregor121]

thx. I think i can take my test now.

[chazdave1]

God u good. do u do any private lessons.

[bradder555]

@khanacademy i think these videos are great, these are perfect revision since i last did this sort of maths a couple of years back (plus i tend to do things in the laplace domain) i was wondering, your using a graphics tablet? what software are you using to make the video?

many thanks

[lovejinahpark]

is that initial condition given? or do i have to solve that out?

[MiEsHhTaA]

Your videos are very helpful! Could you make one with an example using cos & sin?

[ZhangyXD]

to solve 4r^2 - 8r + 3

you can do 4r^2-2r-6r+3 then solve

It's easier =p

[gefallt]

HAHA, 2nd year engineering physics student, and this is a lifesaver..... my teacher is illiterate.

Owe you big time man!

[ehypersonic]

all this videos are helping me a lot, thanks khanacademy :)

pd: i'm taking this at second semester (1º year) of undergraduate physics here

[psychedelikaj]

Thankyou Sal!

1st year 2nd sem geophysics here and this stuff is all new to me.

[jcobaltss2005]

im in 2nd year chem and bio engineering and we are just learning this

[kanitakhaled]

I am in geophysics as well! This is heaven-sent for me. My profs are so garbage (not saying theyre not accomplished- just SO god damn bad at TEACHING when it comes down to it, so may as well be bad at their day jobs)

Something crucially wrong with our education system...

[ishuffle]

no shit. im in university and i think this is a pretty tough topic

[rebelsoldier1860]

im in DE's in my 5th semester as a double major in physics and ME, but i had to sit out on math one semester to take a physics class

[WilliepProductions]

im a sophomore working on a major in ME and this is the easiest class im taking right now....

[twshuman]

from all those comments below...

i have no clue why i'm learning this when i'm only a soph in high school

gawd damn, i dun wanna do this right now

[rorcon]

I did this as a junior in high school. was pretty hard back then for me, so i see what you mean. But this is as hard as math gets in college unless that's what you're majoring in.

[Plutoniummatt]

srsly?...DEs are hardest things in college maths?

[yasinxtype]

Muchas Gracias.Well explained.

[DiZdain]

How about some 2nd order linear homogeneous non-constant coefficient ODE's. I think it's important to point out here that these roots are distinct, however when we have equal real roots (r-2)^2 there will be an additional x in front of y_2 in the answer since the first answer covers both roots. By definition this other answer exists which is c_2 * x * e^(r_2 * x) = y_2. These two answers are linearly independent so it works.

[marimbalove]

You should teach teachers how to teach.

[Constantine769]

@marimbalove You have no idea how bad this should happen.

Teachers don't always deserve the title "Teacher" because too many can't even accomplish it's root word.

[SteadyHaze]

Is this something you'd do in a university calculus class? What level is this at?

[khanacademy]

You would normally take this after taking a year of calculus at the university level.

[clerlic]

We have this in the first year's second semester, if not for your videos, I would probably have to take the tests twice. Thank you!

[gangstasal85]

im doing this in ireland in 1st yr second semester, mechanical engineering

1st semester = algebra + complex numbers + matrices and some other stuff

2nd = calculus + differential eqs with euler + newton stuff + vector calculus

3rd semester = some more diff eqs + probablility/stats + runga kutta and sutff

4th semester = advanced calculus

and thats the end of math

[seen8]

@khanacademy you are a genius...even though this is something that isnt dat crazy but love the things u are doing for us...

I salute you for that!!!

and May god bless you

[matthewpetersen7]

@khanacademy dayumm serious? after first year uni? we do this at a level if i am not mistaken

[notnever5]

@khanacademy i found this after 2 months in my first university calculus course

[hs1white]

Here in America the college classes usually go:

1st semester- derivitives, intro integrals

2nd semester - volume integrals about an axis, taylor series, intro to differential equations, polar coordinate equations w/ calc

3rd semester - vector calculus, partial derivitives, surface integrals

4th semester - all kinds of differential equations

im not positive that this is standard but it seems to be from people ive talked to, and i might of forgotten stuff.

[haider87]

This is second semester stuff at UC Berkeley

[moreoriginalusername]

yay I'm going to Berkeley next fall. =)

[gambuzo]

Marvelous !!!