❖ 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

[@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

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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!

[@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.

[@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.

[@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!

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

[@JordanBl]

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

[@shoskq7206]

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

[@sediye]

life saver, you deserve a Nobel prize

[@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 ;)

[@roshanshihab8515]

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

[@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

[@rebelgamer]

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

[@xelvince]

Eternal Value. Thank you PatrickJMT.

[@InquiringJoe]

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

[@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.

[@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.

[@xinyun5215]

Engineering Math 2, still here. Love you.

[@electronicjunky6940]

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

[@thakgatsochoma5371]

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

[@patrickjmt]

Glad it helped!

[@dtm876]

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

[@patrickjmt]

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

[@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.

[@f40f50enzof60]

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

[@streamapp]

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

[@jackrecher6986]

it takes like 30 seconds with an E-C haha

[@farizgalang7235]

thanks dude, u save my final test in this semester

[@colinward774]

why even go to class when these exist?

[@sbk1398]

You don't :)

[@everbtw]

pop quizzes 😥

[@6subswith0vids80]

Fugging attendance ):

[@con_el_maestro3544]

Degree

[@aizazhashmi9433]

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

[@8aL3mEeL8]

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

[@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)

[@jeremiahbenton7907]

Excellent example. Very similar to what you will see

[@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

[@abdulhalimaslanacier3847]

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

[@notadeity]

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

[@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)

[@Sam-kc5np]

Insightful. Thorough and detailed. Good shit!

[@egedenizrodoplu7954]

wow nice solution. greeting from Bursa 16 🐊

[@pancakeofdestiny]

You are, as ever, a life saver

[@na3ak4]

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

[@lifeofmine6342]

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

[@patrickjmt]

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

[@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.

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

[@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

[@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?

[@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!

[@gustavotintaya2078]

YOU MAKE BETTER WORK THAN MY STUPID PROFFESOR IN COLLEGE.

[@frankym5099]

Thanks for all the helps in math !!

[@J0hnH4l0]

man just had to be left handed

[@FidaHussain-ue1jq]

Thank you soo much sir , For such an informatic example

[@plasmalady9871]

Fantastically helpful video

[@matthewnovak7351]

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

[@sharonshavilet5800]

Excellent teacher🙏🤝

[@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.

[@kawanabdullah7539]

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

[@Pel0r]

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

[@shahadmadani2124]

Thank you for saving my life

[@lesegomokgabudi5798]

THANKS BRO .... u are a superhero

[@andikafadhlansyah2411]

thanks a lot Patrick!

[@LockiePockie]

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

[@kavishamahabir8340]

you are a blessing

[@esmeraldavargas7180]

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

[@thamannaak4157]

Thanks a lot 🤝

[@3bdullah830]

I'm taking this topic now in the third year of engineering college

[@NathanWiegman]

You said to multiply by dx. While it is functionally the same, it is not at all what is actually happening and I worry that it might confuse other people in higher order equations.

[@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

[@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?

[@jkgadgets3826]

Your videos are so good

[@yousifsalam]

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

[@yetmgetaredahegnkassaye]

Man you are still legend

[@patrickjmt]

thanks homie

[@streamapp]

Also be careful about saying e to the something is an arbitrary constant. The constant has to be positive so you are losing information when you say that.

[@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.

[@patrickjmt]

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

[@oninsfirred]

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

[@stephanbotes5865]

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

[@patrickjmt]

no problem :) hope i made some sense :)

[@hijabzehra4589]

Helped a lot, thanks.

[@tomcarpino7946]

You're extremely helpful.

[@mrfahadalazmi89]

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

[@1cubsfan100]

Yes the videos from 2006 are helping

[@jessicabelfield]

love your videos! thank you thank you!

[@patrickjmt]

happy to help!

[@patrickjmt]

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

[@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.

[@Aaronleung1111]

VERY CLEAR! THANK YOU!

[@raymondzhao1971]

Isn't the general solution y=C_1(y_1)+C_2(y_2) where you plug the y that you just solved for into y_2?

[@abdussalamabubakarkura6315]

thank you sir I am very greatful,

[@krillinslosingstreak]

Since C_1 is exp(C_0), doesn't that mean that C_1 cannot equal zero? Does that matter for the general solution? You can put C_2 as zero, and get the second solution, but not C_1 to get the exact first solution. Although, C_1 can be arbitrarily close to zero. I'm not sure if this breaks anything...

[@IhazBobo]

Havent done this yet but it seems so fun :)

[@leoncage7628]

shouldn't the arbitrary constant C1 be added to e^(lnx^-7) instead of multiplying?

[@alessandrovelazquez1558]

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

[@kestonsmith1354]

I LOVE YOU MAN

[@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

[@beastbaby4849]

Thanks a lot Sir

[@smokeypillow]

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

[@sarajaldawlah]

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

[@rahuljamatia1279]

U helped a lot....thanks

[@lizzy5812]

I thought the general solution was going to be the SUM of the two solutions. Like I thought y2 = Vy1 so the general solution would be Ay1 + By2 = AX + B(C1X^-5 + C2X)