Solving differential equations with the laplace transform

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Intros
Lessons
  1. What is LL{yy'}? What is LL{yy''}? And how do we use these facts to calculate differential equations using Laplace Transforms?
  2. A brief run-down on the steps used to solve a differential equation by using the Laplace Transform.
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Examples
Lessons
  1. Calculating Differential Equations Using Laplace Transforms

    Solve the initial value differential equation:

    y3y+2y=6y'' - 3y' + 2y = 6

    With initial values yy(0) = 2 , yy'(0) = 6

    1. Solve the initial value differential equation:

      y4y+7y=0y'' - 4y' + 7y = 0

      With initial values yy(0) = 3, yy'(0) = 7