Characteristic equation with complex roots

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Intros
Lessons
  1. A very brief run-down on Complex Numbers and Euler's Formula
  2. Using the Characteristic Equation with Complex Roots
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Examples
Lessons
  1. Determining Complex Solutions to the Characteristic Equations
    Find the particular solution to the following differential equation:

    y2y+2y=0y''-2y'+2y=0

    With initial values y(0)=0,y(0)=2y(0)=0, y' (0)=2
    1. Find the particular solution to the following differential equation:

      y+4y+8y=0y''+4y'+8y=0

      With initial values y(π2)=1y( \frac{\pi}{2} )=-1, y(π2)=1y' (\frac{\pi}{2})=1
      1. Find the particular solution to the following differential equation:

        y2y+4y=0y''-2y'+4y=0

        With initial values y(0)=4y( 0)=4, y(0)=5y' (0)=5