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