assignment Homework
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.
- \(\ddot{x}-\dot{x}-6x=0\)
- \(y^{\prime\prime\prime}-3y^{\prime\prime}+3y^{\prime}-y=0\)
- \(\frac{d^2w}{dz^2}-4\frac{dw}{dz}+5w=0\)