❖ Reduction of Order: Basic Example in Differential Equations ❖

[@msjahun]

Real heroes don't wear capes, real heroes tech you Differential equations.

[@4chance610]

Grammar is optional?

[@Twothron3]

i think im dizzy after watching this :P

[@cmprice11]

i lov teching studens maths

[@joelu3691]

this dude literally teaches everything in mechanical engineering

[@benjamincalloway]

Reads book: *thonking* Attends lecture: *visible confusion* Watches patrick: R E V E L A T I O N

[@patrickjmt]

you are too kind :)

[@mexicanwootwoot]

Invest in Stonks.

[@holopleasures4011]

Sometimes it is just seeing the same thing multiple times from multiple perspectives.

[@chandlerinman4393]

From High School Algebra 2 to College Diff EQ, you're always there. Thanks for all your help! I wonder if you have any videos related to Real Analysis.

[@patrickjmt]

+Chandler “Thunder99879” Inman not many

[@hemantslift]

Heyyy

[@eves.9]

I am literally crying tears of joy. Thank you for all you do. You are the reason I will pass this class. Not having in-person lectures during the quarantine means my professor is sending us bad videos which I can't understand as well as your videos.

[@patrickjmt]

tell her/him to send mine as well :) glad i could help!

[@patrickjmt]

i like all of it :) i like the beauty of pure math and i also like being able to actually use it for something as well!

[@JordanBl]

And here, ladies and gentlemen, we have a man saving the day from almost four years in the past.

[@vidgami46]

You make this sound so much simpler than my Engineering Analysis professor does, and you don't just copy from a textbook! Thanks for what you do.

[@BasketOFmuffins]

You know math is difficult when you understand every method and then you get to the test and draw a blank. And for that reason, I know for sure that Patrick is gifted.

[@orchidtulip1234]

woww those 'v's look like square root signs, great video regardless

[@missempoi1976]

+Richard Butler yeah, at first im a little bit confused. O.o

[@jazzm5557]

Richard Butler ahhh damn, once seen can never be unseen D: 😂

[@tomoguitaro]

I hear v but see sqrt

[@colinward774]

why even go to class when these exist?

[@sbk1398]

You don't :)

[@everbtw]

pop quizzes 😥

[@6subswith0vids80]

Fugging attendance ):

[@con_el_maestro3544]

Degree

[@patrickjmt]

it did not seem as though people were that interested - more people keep asking for differential equations so i figured i would start making these. i often jump from topic to topic ;)

[@sediye]

life saver, you deserve a Nobel prize

[@roshanshihab8515]

Thanks man, you're a life saver. Exam in 10 minutes

[@rebelgamer]

The fact that you published this video today is astonishing. I have a math midterm that includes RoO in a few hours.

[@shoskq7206]

You taugh me in 12 min what my lecturer has been trying to teach up in 4 days thank you!!!!!

[@kayshin1237]

Patrick JMT is the God of Math. I seriously can't do anything without him.

[@InquiringJoe]

Great video. It should be in the Differential Equations Playlist.

[@patrickjmt]

this is differential equations. people typically take it after they are done with calculus or in conjunction with their last semester of calculus!

[@xelvince]

Eternal Value. Thank you PatrickJMT.

[@xinyun5215]

Engineering Math 2, still here. Love you.

[@J0hnH4l0]

man just had to be left handed

[@patrickjmt]

v is a function of x. v' is also a function of x. if i let w = v' , you still have a function of x, you are just renaming. for example: let v(x) = sinx. so v' = cos(x). if i let w = v' , then w = cos(x) which is still just a function of x. v is a not a variable.

[@abdulhalimaslanacier3847]

Having seen this, no need to disrupt my sleep for a lecture in the morning anymore :)

[@dtm876]

i'm astounded as to how you make this sound so simple. i'm really grateful. thanks.

[@electronicjunky6940]

its amazing how much easier it is to understand you , than my text book on this subject. Great Job!

[@Sam-kc5np]

Insightful. Thorough and detailed. Good shit!

[@egedenizrodoplu7954]

wow nice solution. greeting from Bursa 16 🐊

[@streamapp]

This is also an Euler Cauchy form, in case you were wondering.

[@jackrecher6986]

it takes like 30 seconds with an E-C haha

[@patrickjmt]

yeaaaaaaaa! austin / round rock are gonna merge into one megalopolis one day anyways.

[@farizgalang7235]

thanks dude, u save my final test in this semester

[@na3ak4]

the Vs looking like sqrts and your notation around 2:10 is killing me

[@sreeharimadhu6885]

Thank you so much sir. I was feeling nervous about my maths exam now I am feeling much more confident after learning the concept through your video.

[@robjones2525]

Thanks for the video! Some advice (take it or leave it)... Elaborate more on when to use reduction of order and why we would even want to use it in the first place. I felt like we rushed into an example. I feel like after watching this video I learned a technique but have only a slight idea of when to apply it.

[@patrickjmt]

i dont really understand your question. w(x) = v ' (x). so, w ' (x) would equal v ''(x). i am not sure why you would need to product rule, or chain rule, or anything else.

[@joshmusic9766]

I wish I found your videos in high school! (Really I mean to say I wish I cared enough to look) you got me through my college physics degree and I have to say thank you! (And give a broke college student donation)

[@aizazhashmi9433]

great method of teaching...you eliminated all my confusion...thanks

[@LockiePockie]

like r u a professor or something in Austin ? I"m in DE right now and these videos are really helpful. thanks alot

[@pancakeofdestiny]

You are, as ever, a life saver

[@BobCliffe]

Hey Patrick, thanks for making everything that you do so accessible for everyone, I'm 15 and you make this sound like the easiest thing ever!! Thanks :) btw, what kind of level is this maths?

[@ahmedredha3721]

happy 21 bro

[@zaklarkin8147]

happy 25 bro

[@f40f50enzof60]

One point of fact- it's actually "homogeneous", not "homogenous". Super helpful video!

[@lifeofmine6342]

How to find 3rd order linearly independent solution of the equation when two linearly independent solutions are given?

[@Pel0r]

Thank you. Can i make a question please? How is Game Theory series going. Should we wait more videos in the near future or you need time?

[@jeremiahbenton7907]

Excellent example. Very similar to what you will see

[@yousifsalam]

@07:15 how were you able to just omit the absolute value symbol from w when you canceled e^ln(|w|)?

[@notadeity]

"Basic". Nice work, your explanation really helped me get a grasp of the method. Thanks.

[@sharonshavilet5800]

Excellent teacher🙏🤝

[@frankym5099]

Thanks for all the helps in math !!

[@robertsishuba6596]

thanks dude really much appreciated .. i am in south africa but you turned into my lecture by just a click ..

[@ToTheMaxx]

Cant we just hire this guy to do all the maths we need for engineering?

you definitely helped me understand this concept and how to start on this. Thank you

[@MagnusonX]

I am not entirely clear how we identify the Second Solution as x^-5. Please explain.

[@XxKo0loxX]

Lars Magnus Earlier on he explained that the question gave one of the two solutions. In this case the given/known solution is x. That is why he multiplied v to x. The standardized procedure is multiplying v into a known solution.

[@ceoofnothing3211]

thank you so much, i cant learn from textbooks. i need to see it done so i can follow the steps. and now i finally get it.

[@patrickjmt]

reading a textbook can be tricky! glad i could help

[@henryfob395]

I think in order to use reduction of order your DE has to be homogeneous namely where g(x) has to be zero. And reduction of order it used when you are given one solution to the DE and need to find the second solution

[@T.Zy.]

Should be x^-3 though for the last step as we do: 1/(x^4) * x = 1/(x^3) = x^(-3)

[@sand-barry]

+whyisthisnicknamebad That is 1/(x^6), I think you're mistaking the exponent -6 for a -4 x^(-6) * x = x^(-5)

[@gustavotintaya2078]

YOU MAKE BETTER WORK THAN MY STUPID PROFFESOR IN COLLEGE.

[@thakgatsochoma5371]

Watching hours before my exam and i can say this made everything look easy thank you!!!!!!!!!

[@patrickjmt]

Glad it helped!

[@plasmalady9871]

Fantastically helpful video

[@patrickjmt]

no problem :) hope i made some sense :)

[@sarajaldawlah]

Hey Patrick, U R AWESOME! Thank U so much I do really appreciate it.

[@oninsfirred]

Hello Patrick, What if there is no given solution on that differential equation? how do you formulate y=vy1?

[@Skip2MeLou1]

Why is the second solution x^-5 ?

[@Tarotoratea]

If you're wondering why it's x^-5 as opposed to x^-6, it's because c1x^-6 was multiplied by x, or x^1 at the end. It is our exponent rules which tell us we can simply add the exponents of x^1 and x^-6 when multiplying to combine them. So: (x^-6)(x^1) = x^-5. ^^ Hope that helps.

[@marcochamba1520]

@@Tarotoratea I think he asked why the second solution is x^-5 not how he got x^-5

[@rongxindou7189]

Great teaching! How should I do if f(x) on the right of equation instead of 0?

[@andikafadhlansyah2411]

thanks a lot Patrick!

[@FidaHussain-ue1jq]

Thank you soo much sir , For such an informatic example

[@iloveitgirlandR5]

When should you use this method? like for a 1st 2nd order or a linear non linear equation? thanks for the video, great help.

[@Pel0r]

Yeah i understand. Its good to watch for revision anyway. Thank you for your videos.

[@kavishamahabir8340]

you are a blessing

[@jkgadgets3826]

Your videos are so good

[@hijabzehra4589]

Helped a lot, thanks.

[@esmeraldavargas7180]

Can you please show an example of using an Annihilator to solve a high order equation such as Y^6-Y"=t^2

[@lesegomokgabudi5798]

THANKS BRO .... u are a superhero

[@kawanabdullah7539]

the general solution, x^-4 times x equal x^-3, not x^-5....thanks for the video!

[@alexanderjack5937]

At 7:36 it should be w=(e^(lnx))^-7 + e^C Why you have multiplied e^c ?

[@DinsAFK]

+Abdul EE log rules, e^(1+c) = (e^1)*(e^c)

[@patrickjmt]

i sort of refuse to find applications for people who are in DE and engineers. :)

[@utkarshankit]

at time 10:02, the product of (x^-4)*(x) gives (x^-3) but you have written (x^-5) .

[@teresarodriguez9902]

It's x^-6 not x^-4 that's how he got x^-5

[@mrfahadalazmi89]

But the way greatest videos I have watched it thank you again

[@thamannaak4157]

Thanks a lot 🤝

[@smokeypillow]

Shouldn't the second solution be the first solution multiplied by x? Why is it different here?

[@stephanbotes5865]

How do you find the Fundament set of equation if it's not given for these specific equations?

[@jessicabelfield]

love your videos! thank you thank you!

[@patrickjmt]

happy to help!

[@Aaronleung1111]

VERY CLEAR! THANK YOU!

[@patrickjmt]

i think this is easier cause i have to know one less formula

[@PhrozenTiger]

you set w = dv/dx ... doesnt that make w a function of v which itself is a funcion of x? thus using the chain rule when culculating the derivetives... when you say w' = v'' you just derive v as normal, not as if it was a function of x... What peice of the puzzle am i missing?

[@rajivsharma509]

Nice explanation 👌👌

[@alessandrovelazquez1558]

Can I use the cauchy-euler method for this example too??

[@henzofob]

How do you know when to use reduction of order on a D.E. ?

[@shahadmadani2124]

Thank you for saving my life

[@mehmoodhaydar4766]

Can this also be used on nonhomogeneous equations?

[@jessechen4971]

yo pat, how come u didnt mention the formula? it's so much simpler that way =)

[@donaldmoon3527]

Do all the differential equations work out so nicely ? I would like to see an example of something that does not work out so well.

[@jebwatson]

no...

[@guyucu]

r u left handed? or ur using ur left hand so we can see better ?

[@TheAdlcn]

ne alakası var la gerizekalı

[@matthewnovak7351]

why is it so hard for professors to give simple and easy to follow examples like this??

[@ezcollege2964]

Those markers smell bad do you get headaches from them when you film these videos?

[@patrickjmt]

i like to huff them

[@jorddyy]

I thought that y2=vy1, so I did it wrong. But I understand now that vy1 is the general solution. Thank you very much!

[@IhazBobo]

Havent done this yet but it seems so fun :)

[@8aL3mEeL8]

very clear explanation, I got B in my Calc class just because of you God bless

[@patton281]

Since in the previous video, we were given a general formula for any diff eq in the form, y''+py'+qy=0, and we found that if we let w=v', then we get the formula, given y_1(x), to be (y_1)w'+(2y_1'+py_1)w=0, could we just skip all those steps in all circumstances? Because, as soon as you showed the problem, I paused, plugged everything into the formula i mentioned and got the same final answer as you did.

[@rahuljamatia1279]

U helped a lot....thanks

[@sumayyakamal8857]

what does second solution literally mean?

[@jitendrasingh-nd7kq]

How can you sure about that general solution will be "v" time of any particular solution when we know that two particular solution can't be linearly dependent???

[@soumahakase7124]

because "v" is a function of a "x" and not a constant.