Homogeneous Linear ODE's with Constant Coefficients

  • ODEs math bits
  • Oscillations and Waves 2023 (2 years)

    Homogeneous, linear ODEs with constant coefficients were likely covered in your Differential Equations course (MTH 256 or equiv.). If you need a review, please see:

    Constant Coefficients, Homogeneous

    or your differential equations text.

    Answer the following questions for each differential equation below:

    • identify the order of the equation,
    • find the number of linearly independent solutions,
    • find an appropriate set of linearly independent solutions, and
    • find the general solution.
    Each equation has different notations so that you can become familiar with some common notations.
    1. \(\ddot{x}-\dot{x}-6x=0\)
    2. \(y^{\prime\prime\prime}-3y^{\prime\prime}+3y^{\prime}-y=0\)
    3. \(\frac{d^2w}{dz^2}-4\frac{dw}{dz}+5w=0\)