Differential Equations › Section F · Series solutions › Topic F.2
Series solutions near ordinary points
When the coefficients of an equation vary with x, you can still build the solution one coefficient at a time as a power series. Near an ordinary point this always works, and the equation itself tells you how far the series can be trusted.
In this topic
- Solving one coefficient at a time
- Ordinary and singular points
- What is guaranteed
- The method in five steps
- Worked example: a recurrence two steps apart
- Recognising the result
- Worked example: a non-constant leading coefficient
- How far the series reaches
- Airy's equation
- Common mistakes to avoid
- Key takeaways
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