Characteristic equation with complex roots

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

    y′′−2y′+2y=0y''-2y'+2y=0

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

    y′′−2y′+4y=0y''-2y'+4y=0

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