Consider the initial value problem [math]

  1. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of [math] by [math]. Do not move any terms from one side of the equation to the other (until you get to part (b) below).

    [math] help (formulas)

  2. Solve your equation for [math].

    [math]

  3. Take the inverse Laplace transform of both sides of the previous equation to solve for [math].

    [math]