Laplace and ODE @drpeyam

Uploaded October 2024 | Updated September 2026, 1 week ago

the fruit of our work: Laplace and ODE

We use our knowledge of Laplace transforms to finally solve some ODE. You do this by applying the laplace transform and then using our Laplace miracle to get an algebra equation and then using partial fractions from calculus to find the inverse Laplace transform. Voila, no guessing involved, this gives you a really elegant way of solving differential equations, enjoy!

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$Laplace and ODE the fruit of our work: Laplace and ODE We use our knowledge of Laplace transforms to finally solve some ODE. You do this by applying the laplace transform and then using our Laplace miracle to get an algebra equation and then using partial fractions from calculus to find the inverse Laplace transform. Voila, no guessing involved, this gives you a really elegant way of solving differential equations, enjoy! Subscribe to my channel: https://youtube.com/drpeyam Instagram: https://www.instagram.com/peyamstagram/ Teespring merch: https://dr-peyam.creator-spring.com/?$

$life changing partial fractions trick$

$what is the plastic ratio? what is the plastic ratio? I define the plastic number and explain its properties, first as a cubic equation and a Fibonacci sequence to count bunnies, then as a fractal cube root with self similarities, and finally a cool formula with hyperbolic cosine function substitution. This is a cool journey through algebra, polynomials, inverse functions, and calculus. Proof that I did it before mathologer: https://youtu.be/SMeNVyJjd2o 0:00 Introduction 0:36 Fibonacci 1:45 Fractal 3:10 Hyperbolic trig Calculating hyperbolic trig functions: https://youtu.be/My2S-xbLPG0 YT channel: https://youtube.com/drpeyam TikTok channel: https://www.tiktok.com/@drpeyam Instagram: https://www.instagram.com/peyamstagram/ Twitter: https://twitter.com/drpeyam Teespring merch: https://teespring.com/stores/dr-peyam$ $solving a fractional differential equation$