Uploaded May 2022 | Updated September 2026, 1 week ago
the extraordinary Laplace method for solving systems of ode. We solve a system of differential equations in a direct and easy way, without the use of linear algebra or eigenvalues. This method uses the laplace transform, very widely used in physics and engineering, which turns differentiation into multiplication. It is defined with an integral with exponential functions, and is very suited for convolutions and dirac delta distributions. To solve this, we use L on both sides and solve for the solutions using Cramer's rule. This is good when the two solutions or particles are coupled, and can be used for example to describe planetary motion in physics.
0:00 Introduction
1:15 Laplace Transforms
3:36 Cramer's rule
7:00 Solution
Laplace integral: youtu.be/a5l4owYxjRw
YT channel: youtube.com/drpeyam
TikTok channel: tiktok.com/@drpeyam
Instagram: instagram.com/peyamstagram
Twitter: twitter.com/drpeyam
Teespring merch: teespring.com/stores/dr-peyam
the extraordinary Laplace method for solving systems of ode. We solve a system of differential equations in a direct and easy way, without the use of linear algebra or eigenvalues. This method uses the laplace transform, very widely used in physics and engineering, which turns differentiation into multiplication. It is defined with an integral with exponential functions, and is very suited for convolutions and dirac delta distributions. To solve this, we use L on both sides and solve for the solutions using Cramer's rule. This is good when the two solutions or particles are coupled, and can be used for example to describe planetary motion in physics.
0:00 Introduction
1:15 Laplace Transforms
3:36 Cramer's rule
7:00 Solution
Laplace integral: youtu.be/a5l4owYxjRw
YT channel: youtube.com/drpeyam
TikTok channel: tiktok.com/@drpeyam
Instagram: instagram.com/peyamstagram
Twitter: twitter.com/drpeyam
Teespring merch: teespring.com/stores/dr-peyam
