System of differential equations by elimination, ex1

This differential equation tutorial will cover how to solve a system of differential equations by elimination. solve y''+4y'-5y=14+10t: • Undetermined Coefficie...
Check out my differential equation playlists for more lessons and tutorials: www.youtube.com/@blackpenredp...
4 popular ways to factor trinomial: • 4 popular ways to fact...
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[@xavierbolivar-hazboun1347]

Im rocking an A in differential equations right now thanks to you. You da man.

[@blackpenredpen]

Glad to hear 😃

[@tyronekim3506]

Today's students are very fortunate. I never had this kind of video tutorial 50 years ago, much less a professor that not only explains in detail but also shows all of the arithmetic and algebraic steps. Detailed steps were LTS(left to students). My hat's off to this professor. Thanks for the video upload.

[@salsspar2132]

So out of curiosity how did guys pass back then. Ngl I'm not sue I could without these videos. Or at least I never tried. I might of relied on these videos to learn

[@tyronekim3506]

@@salsspar2132 There was no substitute for putting in the time to solve problems.

[@josuequintero-td5gh]

@@salsspar2132 They went to the smart kid and ask them for help

[@coltonstogner4363]

this is so awesome. I love how he's smiling the whole time

[@bocaiden1580]

@Tony Stanley Definitely, have been watching on InstaFlixxer for months myself :)

[@Xx_Eric_was_Here_xX]

for some reason this has been the most difficult section in my entire differential equations class. never did i struggle so much even through the whole of calculus 3. so many steps and execution of arithmetic must be perfect.

[@jakubsz4602]

You are making my Mathematics Degree more enjoyable due to the fact that I get those "It clicked!" moments when watching your videos more often than in my Lectures in UK.

[@blackpenredpen]

Glad to hear Best wishes to you 😃

[@tturi2]

same with engineering lol

[@PunmasterSTP]

How'd your degree going, or did you already graduate?

[@nikola4294]

Man thank you so much for this, i am really really grateful for your amazing videos! Please keep it up!

[@rjanjim]

Can't apreciate it more. Thank you buddy, vety clear and meaningful explanation!

[@williamkoleszar3301]

positive energy and clarity, yet no BS. 10/10

[@eraofworriers2727]

The guy knows what he is talking about and that is why he explains everything simply! Thanks!

[@mohan153doshi]

This is so elegant. I particularly enjoyed the step of differentiating y(t) to get y'(t) and plugging in that value of y'(t) in the equation of x(t) to arrive at a solution for x(t). I was wondering if we would have to go the Xh and the Xp route for x(t). This is really awesome. I enjoyed it Sir. Yes, and the 20 minutes just flew off. One just loses track of time when the beauty of math is presented by you.

[@JamesFinnegany]

This video is amazing and so helpful thank you so much man!

[@OrigamiMaster06]

Great video! I ended up solving this using matrices but this method was super interesting too!

[@jaysadrani3969]

thank you so much for suggesting such an awesome method

[@cheeros]

20 minutes goes by fast when you're learning something new

[@blackpenredpen]

It went by fast as well when i was recording this vid...

[@MegaAdity1]

is the "something new" , an attempt to learn very badly spoken Chinese english ? ...because im struggling.

[@danielgates7559]

Aditya Bharadwaj his spoken English is in fact clear...... I mean, his English has to be good enough to get into UC Berkeley. However, I agree that he is not good at Indian English......

[@letpieau1660]

Aditya Bharadwaj yeah, Indian English is a challenge to learn

[@srockerrr]

Awesome! Thank you so much!

[@JesusGarcia-ox3jj]

thank you so much, I needed this one. I need to hug your mom for making u so smart... please can you do some problems with eigen values and eigen functions for DE.

[@PunmasterSTP]

Elimination! More like "Incredible explanation!" 👍

[@j83lin]

So much better explained than my textbook. Thank you!!

[@abigaildenoyer9968]

THANK YOU SO MUCH YOU ANGELIC HUMAN BEING

[@mohammedfathiramadhan2480]

Thank you man, you are awesome.

[@noraphine]

i'm really thankful ❤

[@tmeryhewjsf35]

This video saved me, thank you!

[@gitayousefi]

SO HELPFUL!!!

[@chunkymonkeymatt]

Thank you so much for the steps

[@thebackendbuilder]

Officially my favorite tutor just cause he's repping SUPREME lol

[@bitterjames]

not cuz he actually knows how to teach?

[@tomatrix7525]

Steve, your awesome man

[@kapilansatkunanathan4257]

thank you learn a lot :)

[@abhimanyookarve5778]

Thank you!

[@jberry4815]

Thank you for saving my life

[@Jamelele]

awesome video!

[@finisilveyra]

You're the best!

[@hichamitani6433]

amazing prof

[@DarkRedZane]

Literally Math God

[@RodolfoRoqueGarcia]

D: !!!! You have gave me a divine revelation!! I can't believe "D" could be used like that! Really easy...

[@stevenson720]

thank you

[@phoebemailwane7949]

Thank you.

[@math-chemtutor6861]

wow my best teacher ever

[@holyshit922]

This system can be also solved algebraically with eigenvalues and eigenvectors or by rewriting it to the symmetric form System of equation dx/dt=f_{1}(x,y,t) dy/dt=f_{2}(x,y,t) can be written as dx/f_{1}(x,y,t)=dy/f_{2}(x,y,t) =dt/1 Will you record video on this ?

[@hidetsuguhiraki2008]

The method you have shown in this video is similar to the method to solve a system of linear equations with two equations and two variables we learned in junior high school. I prefer the use of differential operator D. Thank you.

[@drazynx]

epic. thank you

[@user-wg9np9ty6o]

Good lecture

[@wyattb3138]

I have an engineering problem to solve and I’m actually excited to do math!

[@muhamdhafiz8779]

love from Malaysia

[@physicshub8890]

very smart

[@da.n.j.eevs.ebnath5457]

Please make some videos upon group theory!

[@user-wg9np9ty6o]

Good lecure

[@mugen7628]

"That's it!"

[@NPC-rq9tp]

Nice job

[@blackpenredpen]

good job to you as well!

[@taekwondotime]

Is the eigenvalue method any faster for this?

[@allesisgoed4276]

allah razı olsun paşam

[@loltristanlol]

GOAT!

[@alirezakarimi4977]

Wow;it was absolutely mind blowing.Poor ur students in test😂😂

[@matthijsperabo7282]

He should change his channel name to "blackpenredpenandoccasionallybluepen"

[@cameronspalding9792]

Could you not write it in vector form and find he eigenvalues of the matrix

[@ajjr.7283]

i see the supreme 👀

[@taekwondotime]

Commercials every 4 minutes totally kills the flow. Thanks KZbin!

[@dfhj3084]

👍🏻

[@cantinasongband]

"just like that..."

[@user-oj5zl9fd4r]

Please 😢 What the book you have this information from

[@incalite]

Where did the .. 6t + 2 at 12:03 min come from?

[@DarkPenguins1]

Watch his video in the description. It's Yp and he solves for that.

[@July__-eu5pd]

Is it still possible to convert y(t) and x(t) into some function of x without t with C1 and C2?

[@carultch]

Depends on what solution you get for x(t) and y(t). In special cases, you may be able to do this, such as the case where x(t) = C1*cos(t) + C2*sin(t) and y(t) = -C1*sin(t) + C2*cos(t). In this case, you can get x and y as an interdependent function of each other, with no involvement of t. They will form an ellipse, and there is a general implicit equation of an ellipse in the x-y space, even one that is rotated. It's much harder to do this, when you eigenvalues aren't purely imaginary, as it will be a spiral instead of an ellipse, for complex eigenvalues, and it will be a combination of exponentials for real eigenvalues.

[@Kuratius]

Isn't this about a linear system of differential equations? I thought in the general case the coefficients are functions, not numbers?

[@cameronspalding9792]

When the coefficients are functions, the idea of eigenvalues doesn't work as nicely

[@WRYtube14]

Come on where is the subtitles

[@sayeda.elremaly3939]

😂😂😂omg nice bro ❤❤

[@bboung1004]

It is not difficult but it is complicated.

[@john-athancrow4169]

I got the diff op ok.

[@ratansatya6701]

goat

[@kevinvalenzuela6801]

Why in y(t) you added "6t+2" please help me I can't undertand that,I need to understand that to do my test tomorrow

[@el_witcher]

That's the yp - particular solution for the nonhomogeneous DE.

[@user-ft4xr8gv7o]

A new way to "D",

[@6c15adamsconradwilliam3]

I’d do it with Laplace transformation

[@6c15adamsconradwilliam3]

But there are no initial conditions, forget about it then

[@carultch]

@@6c15adamsconradwilliam3 You set up hypothetical initial conditions. Since this is a first order system with two dependent variables, we only need two initial conditions. Let x(0) = A, and let y(0) = B, as your starting point for using the Laplace transform to solve it.

[@plislegalineu3005]

When you let c₁ and c₂ to be 0, then the answers are linear Nice

[@garfieldismylove]

im very late but can anyone tell me why he puts coefficients in front of the constants c1 and c2? cant you just get rid of the coefficients since multiplying it would just make another constant?

[@carultch]

He puts coefficients in front of the constants, instead of just assigning new constants, because the resulting coefficients are not independent of each other. Instead, they are multiplied by a known constant from each other. Since this is a 2-variable first order system, you can only have two independent arbitrary constants in the ending solution. The eigenvectors establish how the corresponding coefficients in the x and y equations, relate to each other.

[@rovibb2128]

Is it important for x(t) to have (c1)/2 instead of c1 or 2(c2) instead of c2?

[@rovibb2128]

If you could answer ı'll be really happy :)

[@rovibb2128]

BTW great video, thanx

[@jasmine_3333]

لو حليته صح النهاردة هاجي اسويلك صبصقرايب

[@ianrobinson8518]

At 4:30 he says “multiply by (D-3)”. This is not correct. One is “applying” the operator (D-3) to what follows. It may look like multiplying but it’s not. It’s just shorthand for (d/dx - 3) f(x) which is means df(x)/dx - 3f(x). Nonetheless the D operator can be applied using the laws of arithmetic. For example (D-3)(D-4) is equivalent to D^2 - 7D + 12. D^2 means 2nd derivative. The use of the D operator like this was taught a long time ago (before computers) as a part of the subject finite differences. Likewise the operator 1/D means the antiderivative (or integral).

[@gardenia3043]

thank you.

[@20vturbopower]

If D is a derivative operator, than what does 4D (for example) even mean? Isn't that incorrect notation? Am I mistaken here in thinking this way? Thanks!

[@20vturbopower]

DashinBlu that would then mean D^4 not 4D. Those aren't equal obviously. My point is to say that 4D is in fact incorrect mathematical procedure. If D = d/dt, then I should be able to replace it back in at any time and it should still make sense.

[@earendilthebright5402]

Yes but also you manipulate d/dt like it were a fraction with u substitution, even tho its technically not.. I think its just a useful tool

[@budtastic1224]

4D = 0.... so nothing to worry about there

[@psilvakimo]

@@budtastic1224 That would equal a constant for a solution.

[@ianrobinson8518]

D is an operator (differentiation) on what follows. 4D means first differentiate then multiply by 4. It’s equivalent to 4D.

[@psilvakimo]

I have a bachelor's and master's degree in math. This kid is great.

[@john-athancrow4169]

I thought mult.

[@sonuaryan5287]

How to find c1 and c2

[@carultch]

You'd plug in initial conditions in place of x and y, and solve for the corresponding c1 and c2.

[@sonuaryan5287]

​@@carultch thanks after one year I had learn but thanks.

[@magdalena4258]

What would happen, if we had 10 instead of 10t? I mean (D-3)*10=0-30? Or just simple =0? Cause I'm trying to use this method in a different example and I don't know what to do here :( When I'm writting =0-30 my solution is not correct

[@carultch]

One way you can do this, when you just have constants, instead of functions of t, is to assign capital X and Y as temporary variables, centered on the origin. Consider the example: x' = 3*x - 4*y + 5 y' = 4*x - 7*y + 10 (I chose 5 and 10, so my intermediate step is kept simple) Define capital X and capital Y, such that X=x+a, and Y=y+b, in order to eliminate the constants of 5 and 10. Since a and be are just added constants, X' = x', and Y' = y'. Thus: X' = 3*(X - a) - 4*(Y - b) + 5 Y' = 4*(X - a) - 7*(Y - b) + 10 Expand: X' = 3*X - 4*Y + 5 - 3*a + 4*b Y' = 4*X - 7*Y + 10 - 4*a + 7*b We'd like our values of a and b, to eliminate the constants entirely. Thus, this produces a 2x2 system to solve for a & b: 5 - 3*a + 4*b = 0 10 - 4*a + 7*b = 0 Solution: a = -1, b = -2 Now we can solve the DE system: X' = 3*X - 4*Y Y' = 4*X - 7*Y Eigenvalues: lambda1 = -5, lambda2 = 1 Eigenvectors: V1 = , V2 = Solution for X & Y: X = k1*e^(-5*t) + 2*k2*e^t Y = 2*k1*e^(-5*t) + k2*e^t And undo the shift, such that x = X - a, and y = Y - b: x = k1*e^(-5*t) + 2*k2*e^t + 1 y = 2*k1*e^(-5*t) + k2*e^t + 2

[@Dave-yb3ng]

The book from which this problems was taken from is absolutely garbage at explaining the elimination of x, burn in hell snider et al

[@nabarun83]

is it just me or is his accent really irritating!?!?!?!😡😵😵😵

[@blackpenredpen]

Just you.

[@nabarun83]

blackpenredpen i know that I'm being very superficial here...ugh!!! sorry!

[@blackpenredpen]

Nabarun Kashyap Ok.

[@bart4950]

Overusing smileys is more irritating in my opinion