Second-Order Non-Homogeneous Differential Equations 2 (KristaKingMath)

[@kyshamwandawiro734]

You are the blessing I have been looking for all my life. Kenyan lecturers wouldn't care less whether you have understood or not. They move at their own pace, mostly quickly, to complete the curriculum without enquiring whether the students have understood or taking time to explain why and how each step comes about. Krista, you are truly an answered prayer.

[@DasnarkyRemarky]

Oh my God you're such a lifesaver. I can't even begin to describe to you how much better i understand the inns and outs of 2nd order non homogenous differential equations because of you. Thank you so much. I'd be so lost without you.

[@kristakingmath]

DaSnarky Remarky I'm so happy to be able to help, and so glad that these problems are making more sense for you!

[@MrPANICbutton]

There are a lot of different tutors on KZbin. I typically like to cycle through khanacademy, patrickjmt, and yours! It's nice because you all have different teaching tactics. What I like about yours the most is you take the time to thoroughly explain your topics. Especially where students get lost the most I feel, and you don't mind writing out the simple algebra steps that we all tend to mess up on. Your also very clean and organized, makes it easier to follow. Thanks for the videos!

[@musawwerrasheed994]

You are a greatest teacher i have ever seen. If there were so many like you on this planet, this world would become a heaven. :)

[@kristakingmath]

when we solved for r we found two solutions to the differential equation, r=-2 and r=-2. when you find two solutions with the same value, you have to include the extra x in the formula to distinguish the terms from one another, otherwise you won't be able to find the particular solution. if you get two solutions for r and the solutions are different, then you can use the same formula but without the extra x. hope that helps! :)

[@kristakingmath]

@flexinou I got the correct answer, and I'm failing to see anything wrong with my steps. I don't know why you got different values.

[@Alexward1352]

Apart from being fantastic looking, this helped me so much with my maths its not even funny. Paid 20 euro for a maths wizz to help me understand this and he couldn't..17mins and now I can fully do them myself. You're fantastic, thank you!

[@Hash_aerospace]

Awesome! I'm doing my pre-engineering in the UK & the first part we call the complementary function, the second is called the particular integral, then you add them together which gives you the general solution,then if you are given initial conditions for x, y and dy/dx, you sub x and y values inside this to get your first equation for the simultaneous equation, Derive the general sol, plug your initial condition for dy/dx at the front and x and y, make another sim eqn. solve, & get part sol.

[@jcnw92]

This is a great example. You explain things well with a calm voice. Thank you!

[@kristakingmath]

You're very welcome! :)

[@duggan6592]

This and Minute Physics are the two best channels on KZbin. Fair play.

[@J_Nino]

Great video! Love that you take the time to explain your math. That's where most tutors lose me at times because they do the math in their head and I have to go back and figure out how they came up with something. Thank you!

[@KonnerScottMusic]

This channel is incredibly helpful. Please keep up the fantastic work.

[@MisterBinx]

I fell a couple sections behind in this class. This video is saving me. You are the best Krista.

[@kristakingmath]

I definitely will, thanks for watching!! :D

[@zakpbarnes]

missed 2 weeks of Diff E and have a test tomorrow morning over this material. this video and the first on the same subject have saved my tail. Thank you so much!

[@PhibeRCoRe]

You are really gifted in transfering knowledge. Your explanation of things are amazing, I got it all. Thanks and keep doing these videos!

[@xxjhones]

What kind of program or thing you use to draw your graph and numbers while you teach. Iwould like to know if you dont' mind, I like it.

[@EWARTNEPHAWE]

This world need someone like you.

[@jyamijuice9100]

Honestly this was so hard to learn until you came along. You are a light to first year engineering students!

[@kristakingmath]

I'm so glad I can help! :)

[@ragnheiurtraustadottir9989]

A thousand times thank you for this video! I have a Calculus exam tomorrow and have been struggling with these non homogeneous equations all day, but now I completely understand it! I'm gonna subscribe so I can find your channel easily next time I have math problems :)

[@kristakingmath]

Ragnheiður Traustadóttir Hey that's awesome! I'm so glad the videos have been helping... this is definitely a tricky topic! Good luck on your exam tomorrow, I hope you do great!!

[@kristakingmath]

That's so sweet of you! I'm glad it's helping! :)

[@ClerifyGames]

I just learned this at school today, and you explain it waaay more better! Thanks a lot :D Subscribed!

[@kristakingmath]

+ClerifyGames Glad I could help!

[@edwinyeung3572]

Really helpful, clear and in-depth explanation. tysm!!! Keep doing more good stuff.

[@kristakingmath]

+Edwin Yeung You're welcome, glad I could help!

[@beverly6240]

These series are so helpful, thank you so much!

[@kristakingmath]

You're welcome, Beverly, I'm so glad the videos are helping! :)

[@iSKIPUNX]

You are a great teacher. Again, thank you for all the help. I just hope and pray that teachers here in the Phils. would teach us students as effective, patient, and kind as you do. :)

[@kristakingmath]

no, because c_1 is multiplied by e^(-2x) and A is multiplied by cos(3x). if they were multiplied by the same thing, then you'd have a problem, and you'd have to do something fancier than A. :)

[@jeffgettinger2917]

Thank you very much for the in depth example, I am a math tutor and I know when I see a fantastic explanation. Thank you and great job.

[@kristakingmath]

If it's 0 on both sides then you don't have to worry about it. But if it's 0 on the left and you've got a sin3x on the right, then most likely there's something wrong with your particular solution, and you'll need to go back and try a different guess for y_p. Hope that helps! :)

[@krishnaprio]

Thanx for the help !!! the world really needs people like u!

[@kristakingmath]

I always hated when steps were skipped, so I try not to. Thanks for the comment! :D

[@kristakingmath]

@pemulung You're welcome!! :D

[@kristakingmath]

Not yet! Sorry about that!! :(

[@aroonav5628]

definitely really organised and clear explanation. Happy to have found it ! thank u !

[@Edthebanjo]

Have you got any videos where you do proofs...? such as proving that Ae^ax + Be^bx is the only possible general solution to a second order? Or showing how all why the solution is the general solution + a paticular integral?

[@heat3]

for y sub p....why the constant A and B ...don need to upgrade to Ax+C and Bx+C..thanks

[@kristakingmath]

You might need to modify it depending on the left-hand side, but yes, that would be my first guess! :)

[@leemonastesse84]

Great Video! I was wondering if you had a video on the annihilator method? I am struggling with it and have my test tomorrow! Thank you! From Arlington, TX

[@kristakingmath]

It's called "Complex conjugate roots of second-order homogeneous differential equations". :)

[@grandorottcod1]

Hi, can you explain in more detail how do we guess what is the correct possible particular solution of the DE. For example, why did you add +Bsin3x

[@donogam]

I thought it would be enough to just multiply the first part of particular solution with "x", but multiplying both cos & sin does explain the solution wolframalpha gives, so yes, it does help:) Thanks!

[@Marmeladoffe]

What if instead of constants we have functions of x multiplying the derivatives and it is not a Euler/Cauchi differential equation? Do I use the same method to obtain the homogeneous solution?

[@kristakingmath]

I'm so glad I could help! Thanks for the comment!

[@kristakingmath]

interesting! i've seen the different parts of this process called all different things, so it's hard to use standard language that matches for everybody. thanks for the info! :)

[@NazgulMoonblade]

You wouldn't imagine how much this helped me!! Thanks! What kind of program are you using, I like it.

[@peterh.1521]

It is a very helpful video of an example of second order non-homogeneous DE, thx for sharing Krista. /Peter

[@krisitak]

Really cool! Thanks! I have a question. You write that (-9B - 12A + 4B)sin3x = 0.sin3x , because its missing in 130cos3x, but what if sin3x is 0, not (-9B - 12A + 4B) ?

[@kgfcccvvhbbbc7565]

Thank you.. Krista. I use your knowledge for Schrodinger in quantum mechanic. I live in Thailand. Follow you always in utube. You great mathmatic. Thai teacher so kind.

[@kristakingmath]

You're welcome, I'm honored to be able to help! :)

[@kgfcccvvhbbbc7565]

@@kristakingmath you beauty and so genius. So cute knowledge. Thailand likes you.

[@jonathancastillo1715]

Do you have any videos on an auxilary example??

[@ProfessorTortoise]

Hello there. =} I am actually taking differential equations this semester in college. This is chapter four of my book. =} great video! =}

[@heat3]

but c sub 1 and A are constants won't they overlap each other?

[@NazgulMoonblade]

I actually passed the test and I have you to thank! Do you know what the black tablet program is called? I use a program which makes it look I'm writing in a regular book, which is super boring. Thanks again!

[@donogam]

Hi. Usually i dont have problems solving these kindo f equations, but came across one that which i dont see any logic in. It looks like this: y''+9y=6cos(3x) What i want to know is what you would choose as particular solution. I would go for : Acos(3x)+Bxsin(3x) - - - Which is wrong if you ask wolframalpha. Some1 that can explain me this one?

[@prakashchaudhary4559]

very clear and straight to the point. bravo

[@kristakingmath]

No, I'm sorry... :( I haven't done any proof videos yet, but maybe in the future! :)

[@iSKIPUNX]

Your vid really helped me but i have some problem when i am solving for the general solution of the left hand side with imaginary numbers, what if you have an equation of y''+9=f(x). you would have r^2+9=0. then you would solve for "r" and have an imaginary number (-1)^1/2. in this case you would have r=+/-3i(imaginary). so in that case, how can i solve it ma'am? Thanks

[@SerhiyKapustyan]

hi, tell me please. why do u have an "X" here:C1*exp(r1x)+C2*X*exp(r2x), i mean in previous formulas in was just C1*exp(r1x)+C2*exp(r2x), without an X after C2

[@maddy12318]

Hey I am sorry but the link somehow doesnt work.... I adjusted the spaces between "youtube" and "dot" and tried in different browsers. It gives some error message. Can you please give the video name so that i can search youtube by that name? Thanks again !

[@quartoano2973]

I didnt understand what you do in the right side (130cos(3x)), if you have (in my case) (e^(t)/t) can you tell me how do you do? i would appreciate it very much :) thx

[@maddy12318]

Hey, your videos are awesome... I just had a quick question, what if the roots of the "r" equation are complex... Can you advice how to proceed in that case? Thanks in advance !

[@kristakingmath]

You're welcome! Glad I could help! :)

[@mkusasakala3861]

Extremely helpfull as usuall!! what if i have the y' terms in my equation missing e.g y"+ y=f(x) should i treat such an equation as Second-Order Non-Homogeneous Differential Equation?

[@kristakingmath]

You're welcome!! :) I'm using Sketchbook. It's pretty cool! :)

[@DelJuvePiero]

Just solved a problem I've been stuck on for three hours. Thanks!

[@orororororororo]

great video, thank you very very much! :D.... one cuestion, how can i do it if i have sen^2(x)? how is the Yp?.... Again, thank you very much! :D

[@AmeerAK95]

My final is in two days and you saved me. Thank you ! :)

[@kristakingmath]

You're welcome! Good luck on your final!!

[@kristakingmath]

Awesome! So glad I could help! :)

[@charliewillson1005]

integralCALC i need help with my calculus... can you integrate my natural log?

[@HUCERBH3947]

thank you for the good explanation but how you multiply the first eq by 2 and the other eq by 5????

[@kristakingmath]

You can always perform any operation to an equation, as long as you do it to both sides. For a random example, if you have the equation 2x=8, you can multiply both sides by 6, and make the equation 12x=48. Notice how it doesn't change the value of the equation, and you still solve to get x=4. So when I did that, I was multiply everything on both sides of the equation by the same value, so it didn't change the value of either equation. The reason I did it was so that I could get +60B and -60B, so that when I added the equations together, those terms would cancel.

[@Ganamaha1]

If you had say just cos3x instead of 130cos3x could you still sub A in front of the cos3x?

[@kristakingmath]

Yep! You would still use Acos(3x).

[@kristakingmath]

It's sketchbook, and within that you just choose what image you want to draw on.

[@jeanquinay4793]

what if i have tan (x) on the right hand side? what should be my particular sol'n? thanks. nice vid btw.

[@achen94]

Thanks for this great video! One thing that I am still confused about is how exactly you got the first Yp equation? "Yp=Acos(3x)+Bsin(3x). What if it wasn't a trig function how would you find Yp? Or if instead it was 130tan(3x) on the right side? Thanks

[@Sherikovic]

Right at 5:32 she said that "If we didn't add that sin of 3x, we are gonna end up with the sin on the left hand side and no sin of 3x in the right hand side to equate it to" My guess is that because sin and cos are both phase shifted functions of each other, you have to add them both to lay out all the possibilities of all the solutions.

[@achen94]

lol thanks, i just took my differential equations exam last thursday, got an A in the class :D

[@kristakingmath]

Andrew Chen Way to go Andrew!!! :D

[@ArrowWaters]

***** integralCALC Andrew Chen So if tan3x was on the RHS would you need to add a sec^2(3x) for your particular solution or would you split it into sin3x/cos3x and do something else...?

[@miqdaadwalji]

one word.. PERFECT!! thanx a million

[@SALMANP1]

how would you solve = y''+4y'+4y=8

[@jeremyho6139]

U R A LIFE SAVER LADY !

[@kristakingmath]

I always hated when certain steps were skipped as well, so I do my best not to do the same. :) Glad you like my style!

[@kristakingmath]

I'm so sorry! I'm not familiar with that method, and I don't have a video on it. Wish I could be more help, but I'll keep my fingers crossed that your test goes great tomorrow!! :)

[@taiki1994]

Great video, no mucking about and on point

[@kristakingmath]

You are so welcome! :)

[@cerenalir9423]

Great video thanks a lot :) what do we do when we have for example y(0) = 0.7 y'(0)=-11.8 will we used them to find c1 and c2 ?

[@drcaligaridane]

I have a test based on this 2 days from now and I was studying all alone and only fucking myself over it, watching your videos made it a lot easier. Thanks and keep up the good work. From a brazilian watcher :)

[@kristakingmath]

Ariss I'm so glad the videos were helpful, thanks for letting me know!

[@BlissAden]

you are a genius you just taught me a new way to get rid of the denominator thank you! say if the right hand side was equal to cosx? do I imagine there to be 1 x cosx? to work it out just as you done for 130? Then when you said A and B are constants so I assume you made it equal = 1 then you took the 3 from cos3x and ended up with -3Asin3x and 3Bcos3x is that right? you explain this round around 5:50 7:10. this is before solving a value for A and B looks to me you completely ignored the 130 in the beginning and you used it at the end. my problem is right hand side equals to cosx so do i assume that there is a (1)cosx to later work on the simultaneous equation?

[@InvestorSpeed]

How come you would not add a C constant to the particular? Reason i ask is because you did it in your last video.

[@kristakingmath]

The last video probably had a different particular solution. If it was a polynomial, like x^2, then the particular solution would have been Ax^2+Bx+C. C would have been required, because that's how you represent polynomials in your guess for the particular solution. But in this video, we use sin and cos for the particular solution, and there's no need for that extra constant C.

[@Sharingan1997x]

what if you have Asec(Ax)

[@billyjeff7402]

what do you add to yp if the right side is tan(x)

[@carultch]

You'd use variation of parameters, instead of undetermined coefficients, if you were given a function that doesn't play nicely with diffEQ's. To use undetermined coefficients, you need a function family that either reduces to zero when differentiated like polynomials, or one that stays in the same family of functions, keeping its original complexity, like exponentials, coshes & sinches, and sines and cosines. These functions either scale by a constant or phase shift, or both, when differentiating, but don't become another function entirely like secants and tangents and their cofunctions..

[@joshuarondon4092]

Krista King MY QUEEN THANK YOU!!!!!!

[@kristakingmath]

:D

[@kristakingmath]

Glad I could help! :)

[@Viratkhatri2426]

in question there is only cos3x why we are taking sin3x in particular solution

[@carultch]

Because cosines and sines will shift phase when differentiated, so you have to account for a linear combination of both sines and cosines of the same frequency as your forcing function, for your particular solution. If one of them overlaps with the frequency of a term that is already there, like the natural frequency or damped frequency of the homogeneous part, then there is the phenomenon called resonance, and you'll have to multiply by t, to make a linearly independent term.

[@Donutshop2365]

for Yp, why didn't you multiply con3x by x, since 130con3x has the same term as Acos3x.

[@kristakingmath]

You're not looking for overlapping terms between the original DE and the particular solution. You're looking for overlapping terms between the particular solution and the complementary solution y(x). There's nothing in the particular solution that overlaps with either c_1e^(-2x) or c_2xe^(-2x), so you don't have to modify any terms in the particular solution. I hope that helps!

[@Donutshop2365]

Krista King Oh. Yea. You are right. Thank you. :)

[@kristakingmath]

you're welcome!! so glad you liked it! :D

[@mawandemsi6606]

Ei your videos helped me a lot from maths 2 and i see they will also help me here in maths 3 wow! nice and helpful videos ma ccster

[@kristakingmath]

+Mawande Msi I'm happy to help, good luck in Math 3!

[@Kevinrevenger]

Got a test tomorrow on this, i'm sure to score a B or A now thanks to you.

[@kristakingmath]

+Kevin Ramdial good luck! I hope you crush it. :)

[@angiegonzalez793]

For the last part, you could just use the second equation to set -12A = 5B to solve for B --> it takes a lot less time! :)

[@kristakingmath]

of course! anytime! :D

[@kristakingmath]

Thanks!

[@MrBiohazardboy]

clear and precise, two thumbs up!

[@عمارالرجوب]

Thank beautifully explained can you explain this sol problem yًًًَََ2-6y1+9y=6x^2+2-12e^3x

[@kristakingmath]

When you deal with the left side you'll use the formula for equal real roots, since you end up with (r-3)(r-3). For the right side, your guess for the particular solution should start with Ax^2+Bx+C+De^(3x), but then you need to check for overlapping terms. I think you'll have an overlap with De^(3x), which means you would need to multiply by x to get Ax^2+Bx+C+Dxe^(3x), and I think it might still overlap again, which means you need to multiply by another x to get Ax^2+Bx+C+Dx^2e^(3x). I hope that helps!

[@عمارالرجوب]

Krista King Thanks .Yes helped me ♥ Thank you so much

[@kristakingmath]

Yay! What a relief! :D

[@moviemaker1395]

does this method still work if we complex roots for r?

[@kristakingmath]

Yes, you just have to use the formula for the complementary solution with complex conjugate roots, instead of equal real roots. Other than that, all the steps are the same.

[@moviemaker1395]

+Krista King I tried it and it worked! Thank you very much.

[@kristakingmath]

You're welcome, I'm glad you got it! :D

[@danielforoughi1413]

Hi Krista, If we have e^-2x in yc and we find e^x in yp still we have to multiply e^x by x or we don need it if the powers are different?

[@kristakingmath]

You don't need to multiply by x if the powers are different.

[@danielforoughi1413]

Thank you so much teacher