Differential Equations › Section G · Higher order differential equations › Topic G.2
Homogeneous nth order equations
For constant coefficients, an equation of any order still comes down to the roots of one polynomial. The new features are roots repeated more than twice, complex roots that repeat, and the practical work of finding all the roots in the first place.
In this topic
- The same trial, a bigger polynomial
- Distinct real roots
- Repeated real roots
- Complex roots, single and repeated
- Finding the roots
- Worked example: a cubic initial value problem
- Worked example: a repeated complex pair
- Worked example: every case at once
- Common mistakes to avoid
- Key takeaways
This topic is part of Wuanberri Pro. Checking your access…