Differential Equations › Section G · Higher order differential equations › Topic G.1
Basic concepts for nth order equations
Bending beams and many control systems lead to equations of third, fourth or higher order. The good news is that the theory built for second order carries over almost word for word; this topic sets out exactly what changes when the order is n.
In this topic
- Beyond second order
- The general linear equation of order n
- Existence and uniqueness
- Worked example: the interval of validity
- Superposition and independence
- The Wronskian of n functions
- Worked example: a fundamental set
- Worked example: fitting three conditions
- Nonhomogeneous equations
- Common mistakes to avoid
- Key takeaways
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