Differential Equations - 31 - The Wronskian

[@3amcudi21]

The Lazy Engineer, looks like I found the place to be.

[@thejellyman551]

11 seconds in, "Let me give you a roadmap". MY GOD THANK YOU, I desperately needed that.

[@outrspaced]

Exam tomorrow for me, you teach ODE so much better than my prof! Thank you!

[@pshr2447]

same

[@toi_let954]

@@pshr2447 What did you get? my exam is tomorrow

[@kairatbakirov842]

@@toi_let954 How did you do?? Mine's tomorrow too

[@gellodog]

@@kairatbakirov842 What score did you get? my exam is tomorrow too

[@pshr2447]

​@@toi_let954 I'm late but i got a B and i was more than satisfied 😂

[@Pestam]

You make all these advanced concepts so simple and easy to understand, wish more professors taught like this whole series

[@3bwhabsodium]

EXAM IN 10 HOURS THANK YOU ! , YOU ARE A LIFE SAVER.

[@TheLazyEngineer]

Good luck! Any last minute questions?

[@TheLazyEngineer]

Just noticed the audio sounds kind of strange (maybe its just the headphones I'm using, but ill make sure to fix that). Also for those of you who are waiting on Part 2 of JIT4D, its coming this week!

[@nazarmoroz4228]

Dude I've been stressing out with linear stuff for the past month, turns out my prof was only getting me confused and never explained really, I just watched a couple of your videos and I'm ready for my exam tomorrow.

[@TheLazyEngineer]

Best of luck let me know if you have any last minute questions!

[@debrachambers1304]

How did it go?

[@nazarmoroz4228]

@@debrachambers1304 Passed the class, never ever used Wronskian again, had an internship, then rejected their 80k salary engineering job offer, hopefully graduating in a year. Good luck on the exam Debra!

[@nvirevolution2235]

I liked immediately just because of your voice

[@presentlymine]

This video saved me! Thanks for making it!

[@englishforfunandcompetitio248]

I need a help in series solutions of DE. Please make an exclusive video on the topic.

[@yungmodulus8097]

Well, wish me luck. My final is in 3 minutes. Thanks for your help!

[@TheLazyEngineer]

Yung Modulus let us know how you did! Good luck!

[@AsifAli-oy3vc]

The two solutions y1 and y2 can only be put in general solution only if they are linearly independent. This is what a wronskian measures, whether the two solutions are linearly independent or not. Am I right?

[@TheLazyEngineer]

Anonymous 244 yes that’s right, if you get a wronskian of 0 that implies your solutions are linearly dependent.

[@AsifAli-oy3vc]

@@TheLazyEngineer Thanks

[@DrAxiom-ef6se]

This is awesome. Very helpful. Thank you.

[@redditindia01]

The following information is available for a particular differential equation У2 Уз W= Dy1 Dy2 Dy3 =0 D²y1 D22 D2Y3 2 Check all that applies W is called the Wronskian for the differential equation. V1, V2, and y3 are three solutions to differential equation. The three solutions are linearly independent. The differential equation is of third order.

[@TheLazyEngineer]

This is a very poorly formatted / worded question, and impossible to answer.

[@undyingshithead2182]

If a non square matrix is produced, then determinants isn't applicable right? Is it going to be linearly independent?

[@Tsoenyana]

Can you please give the name of the app/software that you're using, i love it.

[@TheLazyEngineer]

I used a free software called SmoothDraw. I imported a picture of notebook paper as the background.

[@CynicalScorpio]

When is part 2 of the 4th dimension series coming out?

[@MarkMcDaniel]

You did read his name, right?

[@A2Kneettamil]

What app are you using?

[@TheLazyEngineer]

Concepts of Physics A2K it’s called Smoothdraw

[@A2Kneettamil]

The Lazy Engineer thanks bro. Do you suggest any other apps also for this

[@A2Kneettamil]

Bro I am not getting the ruling that is visible in your video. How to get that bro. Please help me

[@TheLazyEngineer]

Concepts of Physics A2K it’s a scanned image of a piece of notebook paper! I just uploaded it as the background image

[@A2Kneettamil]

Thank you bro

[@skierdude6550]

Does it matter what you use as y1 and y2 if so how did you determine which is which?

[@TheLazyEngineer]

skierdude65 no it does not bc if you were to switch y1 and y2 the determinant will only differ by a sign!

[@poloalarzar2184]

The other youtuber cross multiply them, why?

[@redditindia01]

the size of wonkskian matrix gives us info about the order of differential equation true or false

[@TheLazyEngineer]

False

[@redditindia01]

@@TheLazyEngineer Consider an at rest linear system described by y"+25y=2sint+5cos 5t The response of this system will be Decaying oscillations in time. Oscillatory in time. Growing oscillations in time: None of the above.

[@TheLazyEngineer]

@@redditindia01 growing oscillations in time

[@redditindia01]

@@TheLazyEngineer HOW?

[@TheLazyEngineer]

@@redditindia01 look at the homogeneous solution! And then look at the particular solution (right hand side). Have you learned about resonance?

[@flaviusclaudius7510]

Is this property of the Wronskian 'if' or 'if and only if'?

[@TheLazyEngineer]

If and only if! Let me copy a theorem from Boyce: "y=c1y1+c2y2 with arbitrary coefficients c1 and c2 includes every solution to the differential equation IF AND ONLY IF there is a point t0 where the Wronskian of y1 and y2 is not zero. Also: "The solutions y1 and y2 are said to form a fundamental set of solutions if and only if their wronskian is nonzero"

[@flaviusclaudius7510]

Thank you!

[@Ahsan17687]

Great

[@JimmyBrayne]

Maybe use a wacom instead?

[@hannahmorris1835]

Thanks for the help!!

[@frosty8655]

Dude where are you

[@englishforfunandcompetitio248]

👍 great!

[@tomriddle9489]

thanks

[@RAAAHUM]

What kind of engineer are u? By that I mean a mechanical engineer, software engineer etc.

[@TheLazyEngineer]

Mechanical

[@RAAAHUM]

The Lazy Engineer I have a large interest in becoming a mechanical engineer. I just find questions involving SUVAT equations annoying, because I dont know which equation to use at times, but other than that, I really enjoy calculous and statistics.

[@TheLazyEngineer]

I remember having the same problem with those equations back in the day. I reccomend looking at the derivations of those equations (integration), as it will help you understand where they come from and ultimately when to use which one. Mechanical Engineering - at least at the school I graduated from - is the most general engineering. I preffered this because it allowed me to really figure out what i enjoy because I had a wide range of courses. I'd say its a good place to start especially if you enjoy math.

[@zodiark111]

Thanks fam.

[@lemyul]

good job

[@ayan.rodrigo]

I'm screwed :/

[@TheLazyEngineer]

Rodrigo Campos talk to me, Rodrigo! What are you having trouble with?

[@Fubbymaster]

only love for you my friend

[@anthonypascual9347]

thanks b

[@emmashoo3577]

You sound so much like Chris Pratt

[@TheLazyEngineer]

That's funny. Ive also had random people come up to me and tell me I look like him

[@abrarrhine]

You forgot to show Abel formula

[@filoreykjavik]

it's called wronskian NOT ronskian

[@TheLazyEngineer]

Where do I misspell it?