❖ Laplace Transform to Solve a Differential Equation Part 1 of 2 ❖

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Solving a Differential Equation Using the Laplace Transform
In this video, I demonstrate how to use the Laplace transform to solve a differential equation step by step. We start by transforming the original differential equation using Laplace transforms, apply initial conditions, and work through simplifying and solving the equation to find the solution. Whether you're studying engineering, physics, or pure math, learning how to use Laplace transforms is an essential skill for solving differential equations. You’ll get practical techniques on how to use a table of Laplace transforms effectively when working through these types of problems.

What You Will Learn:

How to solve differential equations using the Laplace transform.
Applying initial conditions in the context of Laplace transforms.
The process of manipulating and simplifying Laplace-transformed equations.
Practical use of a table of Laplace transforms for problem-solving.
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Once I graduate and am making the big bucks I'm going to finally be able to pay you for all of your tutoring. It is greatly appreciated.

evanelder
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I have no idea how i would have gotten through Calc I, II, III, linear algebra and now ODEs without your videos! You have been so helpful! Thank you JMT

benjithethird
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Even with videos almost 10 years, they're a massive help during this lockdown with online learning. Big thanks Patrick🙌

gracious
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brah, ur the reason why I'm a successful engineer major... hands down

blarg
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I started watching these videos in high school and now I'm graduating this semester with my Mechanical Engineering degree. Can't say thank you enough for all the great videos that helped with several engineering courses.

ibrahimawadallah
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you sir are a god among us college students with horrible accented professors, thank you.

TheTatumjeffrey
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I watched this video right the day before I had a quiz on Laplace in my Differential Equation class! Prior to watching this I had no idea what was going on in class. Well, guess what I ended up getting a 100 on the quiz and I understand it really well now. Right now I am watching this to review it a little more for my Differential Equation final Tomorrow! :) THANK YOU SAVIOR!

anikahmed
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This is by far the best method to solve for partial fractions that I have seen thus far! 

Leonito
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your videos help me so much. i've been using your math videos since high school and i'm now an engineering major

arikm
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I can never thank you enough for all you have done to help me understand calculus through differential equations. You are by far the clearest teacher I have ever had in math. Not to say my teachers are bad but you cut to the chase extremely well so I'm not bogged down in the details and can concentrate on each step taking place. Your explanations of each step are fantastic also. Thank you, thank you, thank you. You are a precious commodity and using videos allows for pausing, excellent all around.
P.S. You and Paul of Paul's Online Notes should write a math book or 10.

stephenlove
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Amazing, absolutely amazing! I've spent so many hours in lecture trying to understand why all these Y's and y's are appearing everywhere, within the first 5 mins of this video i understood completely!
Thanks so much! Your videos help so many people!!

kurojngyuki
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This step-by-step guide is amazing. Thank you for doing what you do. Can't be more grateful.

melissakhor
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Thank you so much for being such an amazing teacher. I'm from Egypt and your videos have helped me alot. you must continue this you will be a great person by helping people from all over the world.

mustafaalaa
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I've watched your videos for calc 1, 2, 3, and differential equations. Now I am almost done with differential equations and won't get to watch your videos :( They have helped me so much and thank you for the clear explanations :] you rock!!!

ericah
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Very very helpful! Even though you 're english (and I'm danish), you're alot better than my teacher in the university.. Thanks alot!

MartinTrAr
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Great video, any time, any day.You are far more than professors.God bless you!

glaw
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I love you Patrick ! I wish you all the best ! I've finished calc1, calc2 and calc3 and you made that way easier for me

naifalkhunaizi
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Great example and explanation. You're way better than my professor

millertime
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my diff midterm is tomorrow... you are a math superhero!

vastopa
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I forgot how much I enjoy stuff like this

stevesmith