Differential Equations › Section C · Second order differential equations › Topic C.4
Repeated roots
When the characteristic equation has a single repeated root, the exponential method hands us only one solution. A factor of t supplies the missing second one, and this case turns out to mark the exact boundary between oscillating and non-oscillating behaviour.
In this topic
- One root, one solution
- Finding the second solution
- The general solution
- Worked example: a quick return
- Worked example: a fractional root
- How these solutions behave
- The boundary case
- Common mistakes to avoid
- Key takeaways
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