Differential Equations › Section C · Second order differential equations › Topic C.2
Real, distinct roots
When the characteristic equation has two different real roots, the general solution is simply a sum of two exponentials. The skill lies in finding the roots cleanly, fitting the initial conditions and reading off how the solution behaves in the long run.
In this topic
- The first case
- The general solution
- Worked example: an initial value problem
- A zero root
- Starting away from zero
- Worked example: conditions at t = 2
- Symmetric roots and hyperbolic functions
- Long-term behaviour
- Common mistakes to avoid
- Key takeaways
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