Solve differential equation with laplace transform, example 2

inverse laplace transform,
inverse laplace transform example,

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[EagleLogic]

Started the video, paused, went to my marker board and solved it! Then skipped to the end and I saw that I got it right. First time I have solved one of these on my own. Your help has been HUGE! Thank you!

[gigispence]

Spent the last week panicking about Laplace transforms — all of that anxiety vanished after watching this video! Thank you

[ahmed_]

Seriously one of the best teachers I've ever encountered both on youtube and real life. I salute you! Thank you for explaining every detail of your solving and making sure we understand every step you take <3

[Conditional_Finality]

I dont really know why professors in my uni just does not go into this much depth into explaining a single example. The way he teaches me reminds me of my high school teacher who used to make complex problems easily digestible.

[OussamaAbuUmar]

You just taught me more than my professor taught me in a whole semester❤

[bernaskojohnarthur]

Your tutorials are the best just that I'd like to comment on this and a previous video about this same IVP that you should note the way you write your (Y and y). It conflicts as to know which is the laplace and the inverse laplace, Just to help amateur like me. Thank you for your best explanation.

[jemcel]

I want to comment that you can use residue method to get A/s.

To do so, we will consider P(s) = (s^3 + 2s^2 + 1)/(s^2 + 4).

Then, we can differentiate P(s) but we have to divide it by n! where n is the number of times differentiation can occur. (In this case, n= 1) because s is only repeated once.

P'(s) = [(3s^2 + 2s)(s^2 + 4) - 2s(s^3 + 2s^2 + 1)]/(s^2 + 4)^2

From the previous cover-up: s = 0 so we have P'(0).

Then, you can plug 0 into your function. After applying differentiation. You'll be surprised you'll get the same answer for A.

[bizzysiru]

i am a student on uni. at south korea.
thx your class. it a big help for me.

[sanmuga]

Dude You are the best I owe You 20 Marks!!!

[ChefSalad]

You can use cover-up to solve for C and D. Just make s=2i and substitute in. You get 2i+(-7)/(-4)=2i*C + D, therefore D = 7/4 and 2i=2i*C, thus C = 1. BAM!

[Zonnymaka]

Just for the sake of trying the convolution formula i solved the partial fractions s/(4+s^2) + 2/(4+s^2) + 1/[s^2(4+s^4)]. Nice!

[aanchalchaudhary]

your video makes concept crystal clear

[rutgerlight]

You're a good tutor! Im about to comment because i got confused in the A/s +B/s2 ... but you discussed it well ahhaha slow clap*

[skshabbir]

Lots of love for you sir.. 😍😍😍
From Bangladesh..
Your method was super easy to get the problem..

[StraightPathIslam]

Great job man, really good explanation. I think whats so hard to understand is how the denominator is split up into A, B etc. I've taken earlier courses that covered it, but not in the same extend that these exercises need.

[latrellebrown]

I don't sub often, I am about to graduate this year and you earned it!

[stepshred]

Sorry man but I had to....







Pause the video to comment and give you a thumbs up! So glad I subscribed, great work!! Thank you!!

[MrKristian]

Thanks a ton, now I feel very motivated

[andersjohnson]

Watching this during my Calc 4 exam, thank you very much my dude

[marlenabigailrojogarcia]

Me gustaría entenderte en el idioma pero observando tu procedimiento me a ayudado, gracias