I always wonder how come you know every course? I mean, it just hard to understand and able to lecture each and every subject by this level. Thanks for all the great videos and helping me not just to earn better grade but also to understand the material!
Sal, you should have used substitution on that. -3A-5B=0 gives -3A=5B gives B=-3/5A then sub your B into the first equ. in your sys. When you've got the form: Ax + By = 0, its usually faster.
HI, Sal, first of all, thank you very much for your videos, i understand everything in your class but nothing in my classroom. ive got a question: The value of A shouldn´t be -5/17? again thanks a lot for share youre knowledge like this!!!
thank you. I was working on a homework problem for my Linear Systems class and i forgot how to find the particular solution to a sinusoidal input. This reminded me that i needed to use A*Sin(x)+B*Cos(x).
@tadm123 because if you got sin(X) and its first and second dervative u ll have y=sin(x) and dy/dx=cos(x) and d2y/dx2=-sin(x).... if u added them together u ll have cos(x) only so u need a function of sin(x) and cos(x) because the sin(x) is produced from deriving sin(x) twice and ALSO cos(x) once. so u actullay need both cos and sin
You could just differentiate the right hand side of the differential equation twice, and then use every function you find. I think that would be a more methodical approach if you don't want to guess. Sounds bad, but also remember that the coefficients don't matter.
what is the point of adding Asinx + Bcosx when a particular solution? Why not only Asinx, just like we did in the first example where we only considered Ae^(2x)? Thank you!
Just a suggestion: The resulting system for the undetermined presents a 2x2 coefficient matrix and it's obvious from the get-go that we're going to get fractions. A quick way to limit algebraic manipulations that can go wrong is to simply use Cramer's rule: you compute three determinents for 2x2 matrices and obtain ratios very quickly.
Props for saying homogenous instead of homogeneous. They're the same dang word but one requires an extra syllable and sounds goofy, so I'm campaigning for the standardization of the term homogenous! Ironically, this campaign is basically trying to make things more homogenous. Awesome.
Please solve this example...having problem solving thisy"'-3y"+9y'-27y= cos 3xWhile solving perticular solution i got 0= cos 3x...I took yp= Acos3x +Bsin3x
I get more angry every time someone says they're guessing at a solution to one of these problems as if that's how we're expected to go about it. Just call it a formula.
gross mistake at 6:43, actual co-efficients: As the 2nd derivatives of sin and cos are -sin and -cos, y''-3y'-4y=-3(y'+y)=-3{(A-B)sin x + (A+B)cos x} What he wrote is: (-5A + 3B)sinx + (-3A - 5B)cosx
What happens if the function was y''+y=2sinx ? if I do the same step as you did then y''+y for the particular solution would be 0. How do I solve this then?
i'm sorry i'm using this method to solve my exercices and apparently it is wrong somehow, because when i take the derivative of the particular function (right member) Sal does the derivative of g(x)=Asinx + Bcosx while he should be doing the derivative of g(x) = x (Asinx + Bcos)... same thing walframalpha sais (giving me different results from mine), same thing textbooks sais, and the rest of the web sais... please anybody tell me which is the correct method since i'm really confused right now
For all those wondering where he gets the "Acosx + Bsinx" look in your book. If you are taking this course in college then you should have the book which contains all these "Trial Solutions". No need to proof or waste time to explain when it is in your book.
DAMN!!!!! NOW WHY AREN'T YOU MY PROFESSOR!!!! I got some guy from the Mid-East and english ain't his strong suit!!!! If you were our Prof, the school would chip in and buy a CAR!!!!!!!!
does anybody know what the particular solution to just a plain number would be? Ex. y'' - 2y' = 3 + 4sin(2t) the general equation is c1 +c2e^ -2t + 3/t - 1/2 cos2t - 1/2 cos 2t and from the vids i get everything besides how to get 3/t !!!!! 4 hours and still cant figure it out lol please help
thanks a lot, my fucking notes and even the text book they intro us to buy are fucking piece of shit that made things even more complicated and skip too many steps, it's really depend on youtube to help me with this
You might be a teaching genius man, really. Thank you very much for saving my engineering career.
He is bro
12 years have gone, and yet am here, studying what my teacher was supposed to teach me
12 years later and Sal still explains it better than my professor
I always wonder how come you know every course? I mean, it just hard to understand and able to lecture each and every subject by this level. Thanks for all the great videos and helping me not just to earn better grade but also to understand the material!
He has minor degree in math he has lot of experience
Graduated from MIT and Harvard, that’s why
Sal, you should have used substitution on that. -3A-5B=0 gives -3A=5B gives B=-3/5A then sub your B into the first equ. in your sys. When you've got the form: Ax + By = 0, its usually faster.
love u man, got a math-exam tomorrow, its 1:34am here and your talking still makes sense to me.
great job!
How did it went mate?😂
@@akiyamamio810 wow thats 10 years ago 😂 but i think i passed 😅
HI, Sal, first of all, thank you very much for your videos, i understand everything in your class but nothing in my classroom.
ive got a question: The value of A shouldn´t be -5/17?
again thanks a lot for share youre knowledge like this!!!
I have an engineering mathematics exam in the morning. I’ve been trying to figure this out for 3 hours. All fixed in 20 mins on RUclips. I love this
These are amazingly helpful. I love the step by step. Many other videos of mathematical nature assume too much of the viewer and become confusing.
I was sick and missed the lecture on this topic, but you just saved my ass.
thank you. I was working on a homework problem for my Linear Systems class and i forgot how to find the particular solution to a sinusoidal input. This reminded me that i needed to use A*Sin(x)+B*Cos(x).
you made an error when you said that -25/3 - 9/3 = 34/3. It should be -34/3.
@tadm123 because if you got sin(X) and its first and second dervative u ll have y=sin(x) and dy/dx=cos(x) and d2y/dx2=-sin(x).... if u added them together u ll have cos(x) only so u need a function of sin(x) and cos(x) because the sin(x) is produced from deriving sin(x) twice and ALSO cos(x) once. so u actullay need both cos and sin
I love your enthusiasm! It makes rather tedious math much more palatable!
I laughed out loud at "nice ugly number" haha
Wow! Thank you so much Sal! I have homework due tomorrow and I will not have been able to do it without you :D
it gets such a fun algebra when u have on the right side sth like Acos(a*x)
@fermixx me too....i usually do such stupid mistakes...
another one is -1 * -1 = 2 , or something like that -.-
i always giggle when he runs out of space
How to determine "guess"? I can't do that in some problems.
So we carry A paper with all that stuff to the examination room😂😂😂
You could just differentiate the right hand side of the differential equation twice, and then use every function you find. I think that would be a more methodical approach if you don't want to guess. Sounds bad, but also remember that the coefficients don't matter.
what is the point of adding Asinx + Bcosx when a particular solution? Why not only Asinx, just like we did in the first example where we only considered Ae^(2x)? Thank you!
the hard part is always not loosing the negative signs
2*3 = 5 is another really common one i make :S
You have just saved my education thank you sir
Just a suggestion:
The resulting system for the undetermined presents a 2x2 coefficient matrix and it's obvious from the get-go that we're going to get fractions. A quick way to limit algebraic manipulations that can go wrong is to simply use Cramer's rule: you compute three determinents for 2x2 matrices and obtain ratios very quickly.
hahahahaha "Nice...ugly number" cracked me up so much
You make my life easier.. Love your videos!
Props for saying homogenous instead of homogeneous. They're the same dang word but one requires an extra syllable and sounds goofy, so I'm campaigning for the standardization of the term homogenous! Ironically, this campaign is basically trying to make things more homogenous. Awesome.
Please solve this example...having problem solving thisy"'-3y"+9y'-27y= cos 3xWhile solving perticular solution i got 0= cos 3x...I took yp= Acos3x +Bsin3x
Thanks so much for you excellent work.
if you setup a matrix would it give you the same answer though?
8:02 multiply the first equation by -3 and the second equation by 5
Just a little stupid question, but why did you add Bcos(x)?
Because cos differentiates into sine.
I see thx ^^
and sine differentiates to cos
thank you sooo much for these videos!
I get more angry every time someone says they're guessing at a solution to one of these problems as if that's how we're expected to go about it. Just call it a formula.
how do you know when to use A and B instead of just A for the undetermined coeff?
Kyle Chin that is what I want to know??
gross mistake at 6:43, actual co-efficients:
As the 2nd derivatives of sin and cos are -sin and -cos,
y''-3y'-4y=-3(y'+y)=-3{(A-B)sin x + (A+B)cos x}
What he wrote is:
(-5A + 3B)sinx + (-3A - 5B)cosx
Ty for the all great videos
@sagsmaharg Yea, I caught that, too. Hopefully he puts up an annotation.
@khanacademy
I'm not able to solve (D^2 +4)y = cos2x with taking particular solution as Asin2x + Bcos2x. they end up cancelling each other.
i also got the same qn Darrin lin. y bcosx out of all the other trigonometric ratios , bt i think its becoz it is the derivative of sinx
Btw from where do i get that y=Asinx+Bcosx.thx
What happens if the function was y''+y=2sinx ? if I do the same step as you did then y''+y for the particular solution would be 0. How do I solve this then?
same q for me.
yeah he did
AWESOME!!!
at 8:35 shouldn't it be -34 because he is subtracting -9 from -25
Your a life saver
what if there is tanx?
wonderfull
I just llove you!
THANKYOU:::::
Sal why the need to add sinx + cosx, since the solution is in sinx isn't adding doing y=Asinx enough? :o
i'm sorry i'm using this method to solve my exercices and apparently it is wrong somehow, because when i take the derivative of the particular function (right member) Sal does the derivative of g(x)=Asinx + Bcosx while he should be doing the derivative of g(x) = x (Asinx + Bcos)... same thing walframalpha sais (giving me different results from mine), same thing textbooks sais, and the rest of the web sais...
please anybody tell me which is the correct method since i'm really confused right now
Fantastic
My g(x) is 2- 24e^(x) × 5e^(5x).. what do I guess for that? A +(or minus) 24Be^x + Ce^5x doesn't work.
He fixed it silly.
you should definitely remake those videos on a better resolution. your equal sign looks like a square bracket
nice one!
芜湖
Can I guess a value other than cosx
i found an error... A = -5/17 not 5/17 forgot to carry the (-)
my sense of humor is weird, I think. I found it very funny in the way he said the problem was "hairy" at the end of the video. LOL!
Gosh am I weird.
why have taken Bcosx would anyone please explain
there is a method known as variation of the constant.where you dont have to guess any more
y we even used cos
why is the coefficient 0 on 0cosx at min 6:40?
what if 12 cos^2 x?
where did u get the 9 over 3?
I can't find the particular my RHS is = 20COS(KX) then I end up with two equations and three variables :'(
Did you actually watch the whole video or were you just waiting to pick out an error ?
y u r adding with bcosx
never mind, he fixed it! lol
god bless you :)
For all those wondering where he gets the "Acosx + Bsinx" look in your book. If you are taking this course in college then you should have the book which contains all these "Trial Solutions". No need to proof or waste time to explain when it is in your book.
Bahaha 'nice ugly number' xD
DAMN!!!!! NOW WHY AREN'T YOU MY PROFESSOR!!!! I got some guy from the Mid-East and english ain't his strong suit!!!! If you were our Prof, the school would chip in and buy a CAR!!!!!!!!
does anybody know what the particular solution to just a plain number would be?
Ex. y'' - 2y' = 3 + 4sin(2t)
the general equation is c1 +c2e^ -2t + 3/t - 1/2 cos2t - 1/2 cos 2t
and from the vids i get everything besides how to get 3/t !!!!! 4 hours and still cant figure it out lol please help
You are moses
thanks a lot, my fucking notes and even the text book they intro us to buy are fucking piece of shit that made things even more complicated and skip too many steps, it's really depend on youtube to help me with this
james bone man you really need to work on your English ... like right now .
@MrLegna4 nevermind i got it
technoblade?
@07794294114 yes, finishing the video, he corrects himself
5 over 17 nice ugly number!
😂😂
nice ugly number lol
seriously thank you for making this
5 over 17 nice ugly number!
😂😂