Undetermined Coefficients: Solving non-homogeneous ODEs

Hello Dr. Thanks for the lectures, they are really helping to me. I have the ff differential equations and need some ideas on how to start: solve a) x''=-4x^3+4x , b) y''=y^2-y?. Thanks.

how are we saying that y_h +y_p will indeed gives us the general solution ? how do we prove that ?

😂❤

Super good material

I don't get when we have to multiply by t^s when guessing... Could someone please explain it to me?

what if the power of the expo is as the same as one of the roots of the characteristic equation

ily

Thank you sir

really great video, thanks

I taught I will just watch it and leave it but I found it a great video by great lecturer I need to download it fast.❤ U are too good sir

I love you

I fail to understand why you guys explain things better than our own lecturers ,do they want us to fail and not reach their level or what 😊!!@

what should i do with
xy'' - 4y' + 5y/x = x * ln(x)

Y 2prime - 2y prime - 3y =3e^2t = 2y-3y= 1 integral zero goes to infinity 3e^-2at = ye^-at e^at integral zero goes to infinity1/ a-t -= f(t) =v integral 2pie (z^2 + t^2) = 2 integral zt^2+ t^2/2 = z^3 + t^3/3 = 2pie t^2/3 =4/3 piet^3 absolute zero goes to infinite f(t) 1/a-s.

How you not going to solve the last example. disgrace to differential equations.

Sir I have a general question, why we can not solve tan x or cot x function in non homogeneous term in undetermined co-efficients process ?? If anyone who sees my question if you know please response ...

man you are a gold mine

that was really helpful!!!

How is one supposed to find the particular solution to a given equation when literally every combination makes the A variable cancel out so you can't solve for A?

💯

Thank you so much sir

I tried to use the same train of thought with y''-6y'+9y=4e^(3x), but the problem is, when I use Ae^(3x) I get 0=4e^(3x). Online calculators say that the solution should take the form of Ax^2e^(3x), but why is that?

Thank you ! 👌

❤ from india 🇮🇳🇮🇳🇮🇳🇮🇳

kinda confused on how we got -2Ae^-t+Ate^t

Just so helpful. Making my mathematical methods class a breeze!

It has been a while since this video was uploaded so hopefully you still check the comments here. What happens in the case that the characteristic equation has no roots? For example, my book's exercise asks to solve y''+2y'+10y=2e^t.
r^2+2r+10=0 has no roots, so does my non-homogeneous equation have no solutions, or is its solution simply the particular solution?

Thx

you sir are a LEGEND

Man deserves a Nobel prize

How would you solve for the A B C D E when there is five unkowns?

I first watched this video when i was taking a linear algebra course in college. Now a year later i came back to this channel and these video's as a refresher and to prepare for my classes on dynamical systems. Great video!

uhm what do u mean i have to guess 😭 who tf came up with this

u the goat dog, i will dream about this lesson tonight and ace my midterm 💪

I have a quiz today on this topic, thanks for the brief but concise overview of it.

This guy is wayyyyy to excited and hyped up to teach haha

Sir, You are awesome.

You know why this math is fake? Because you're allowed to pretend a non-homogeneous equation is homogeneous in order to solve it. I hate this area of math with a passion.

A4e^2t itu hasil dari langkah-langkah yang mana pak?

Wow, this video cleared up what I didn't understand during my lecture, phenomenal teaching, thank you!

i don't think guessing will help me in my exaam

sending love from Pakistan