Chapter 17 · Ordinary Differential Equations
17.06
Second-Order Linear Equations
For ay'' + by' + cy = 0, try y = e^(rx). The roots of ar² + br + c = 0 give the solutions: two exponentials, xe^(rx) for a repeated root, or decaying oscillations for complex roots.
About 16 minutes
You'll learn to
- →Use the characteristic equation
- →Write general solutions for real, repeated and complex roots
- →Solve initial value problems
- →Describe damping in a spring–mass system