Characteristic equation with repeated roots

Intros
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Lessons
  1. What is the solution to the Characteristic Equation with Repeated Roots?
Examples
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Lessons
  1. Determining the Characteristic Equation with Repeated Roots
    Find the particular solution to the following differential equation:

    y′′−6y′+9y=0y''-6y'+9y=0

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

    4y′′−12y′+9y=04y''-12y'+9y=0

    With initial values y(2)=e3,y′(2)=12e3y(2)=e^3, y'(2)=\frac{1}{2}e^3