Cauchy - Euler Equations and Variation of Parameters Problem 4 (Differential Equations)

[@servius6274]

THANKK YOU, Finally a professor that thoroughly explains the topic and doesnt skips steps and lays it out neatly 💪

[@servius6274]

His channel needs more subs and exposure bc he explains the topics very clearly

[@BlackTshirtMathProfessor]

You’re welcome, fellow mathematician!

[@servius6274]

@@BlackTshirtMathProfessor Haha thank you, I was literally stuck on a Dif Eq problem but this video cleared the way, thank you 🙏

[@deathbyvinyl]

Holy cow, I'm 0:41 seconds in and I'm blown away by the clarity, not only of the lecture, but the video resolution too!!!

[@BlackTshirtMathProfessor]

Thanks! I recorded and edited it in 4K. It was time consuming to get it all in one take but the end result is great.

[@saniamuneer]

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[@saniamuneer]

I am going to share it with my whole class Sir.

[@BlackTshirtMathProfessor]

Thank you!

[@GiddyGibby]

Dankie is thank you , saved me 3 hours of study

[@soniaaa4557]

Great video! I like how you take the time to pause and give us a chance to process the info. Other videos go too fast for me to follow along 😅

[@BlackTshirtMathProfessor]

“Go slower” is one of my favorite tips for teaching

[@Universeoffactuals]

love the quality of the vid fam. 4k is a plus no longer have to squint plus you cut my studying to like 5 mins. basically win win

[@BlackTshirtMathProfessor]

I only provide the highest quality of videos to my fellow mathematicians 🫡

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[@BlackTshirtMathProfessor]

That’s awesome! I’m glad it helped!

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[@scrummyodoole717]

Thank you so much! This exact problem is in my textbook and they skip right over the only step on which I needed clarification. I looked at a bunch of similar problems and they all skip the same step. I can finally move on.

[@BlackTshirtMathProfessor]

Awesome! I’m glad it helped!

[@skyward7903]

Absolutely fantastic! Very clear and easy, thank you so much

[@vaibhavsrivastva1253]

Thanks a ton; may god bless you!

[@mehmetceylanm]

Thanks Professor from Turkey :)🤩

[@BlackTshirtMathProfessor]

You’re welcome, fellow mathematician!

[@mamadetaslimtorabally7363]

You are quite a teacher. Thanks so much for this video. I just subscribed to your channel.

[@kamranahmad6678]

you're the best, professor

[@BlackTshirtMathProfessor]

Thanks, fellow mathematician!

[@skicrazy5700]

Thanks from Afghanistan

[@KB-WORDS]

sir why did you use the variation of parameter method instead of coefficient method, as i know usually when the G(x) is tan or sec or some complex function we use the parameter, but in the coefficient we usually use it for the e^x, thanks in advance

[@alsendy2936]

Here you can’t use undetermined coefficient because the coefficient of y’ and y are functions of the variable x .

[@vanshutyagi4513]

Thanks from India 🇮🇳🫶

[@kevinsellers7566]

Great Video ❤. Thank you.

[@mohamedalsaedi4720]

very useful👏

[@modernpendu987]

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[@e.m.1766]

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[@taipowerbuilding1641]

THANK YOU 🙏

[@aidanshum4991]

this is so good

[@BlackTshirtMathProfessor]

I only provide the best for my fellow mathematicians.

[@manojsurya1005]

I got a doubt,Y did u use variation in parameters in this problem and not in the previous ones , we could hav stopped at Y=c1X+c2X³, is it due to presence of a function (2x⁴e^x) on the rhs side?

[@BlackTshirtMathProfessor]

You’re right. Since this is a nonhomogeneous differential equation we need to use variation of parameters to find the particular solution. The previous problems were all homogeneous so there’s no particular solution to find.

[@manojsurya1005]

@@BlackTshirtMathProfessor ok thx

[@edismb]

Hello! What would be the formula for U1(x), U2(x), U3(x) and the wronskian if we had 3 y's as solutions? Thank you!

[@BlackTshirtMathProfessor]

That’s a great question. I don’t have a video on that but this resource explains how to generalize variation of parameters to higher-order ODEs: math.libretexts.org/Bookshelves/Differential_Equations/Elementary_Differential_Equations_with_Boundary_Value_Problems_(Trench)/09%3A_Linear_Higher_Order_Differential_Equations/9.04%3A_Variation_of_Parameters_for_Higher_Order_Equations

[@edismb]

@@BlackTshirtMathProfessor Thank you! Have a great day!

[@edismb]

@@BlackTshirtMathProfessor It just came to my realisation, thank you, again, for responding so quickly! I got my midterm next week and didn't understand this part during my uni course! Have a great day!

[@BlackTshirtMathProfessor]

You’re welcome, fellow mathematician!

[@akinyimildred6012]

Kindly solve the one with degree 3

[@TheNutYT]

how do i find g(x) if i have a third order DE? the DE im given is x^3 y''' + x^2 y'' = x^3. i take this class in the fall and am just trying to solve a question a friend gave me, lol

[@BlackTshirtMathProfessor]

This can be reduced to a first-order ODE. Try using the substitution z = y’’, which implies that z’ = y’’’

[@saturday1971]

5:43 감사합니다

[@saturday1971]

Nice lecture So sad bcuz i cant understand all of this due to my Eng skill

[@FlipperSkipp]

Good sir I will kiss you on the lips, thank you for your service

[@kyutlily3041]

LMAO