Solving Initial Value Problems using Laplace Transforms- Basic

In this video, I solve differential equations using Laplace transforms and put forward the basic theory. I only use basic fundamental Laplace transforms and inverses, but the method will hold for any functions where we will use Laplace Transforms.
00:00 Introduction
01:27 Laplace transform of the derivative
02:23 Proving the Derivative
05:12 Laplace Transform of y"
06:06 Example 1- First Order IVP
08:29 Example 2- First Order IVP
13:59 Example 3- Second Order IVP
17:25 Review of the Process
18:22 Conclusions

In case you need some background before you begin:

Defining the Laplace Transform:    • Defining the Laplace Transform  
Finding Laplace Transforms:    • Finding Laplace Transforms  
Inverse Laplace Transforms:    • Inverse Laplace Transforms - Basic