Differential Equations › Section C · Second order differential equations › Topic C.6
Fundamental sets and the Wronskian
So far we have trusted that two different-looking solutions are enough to build every solution. This topic makes that precise: a single determinant, the Wronskian, decides whether a pair of solutions can meet every possible initial condition.
In this topic
- The question left open
- Existence and uniqueness
- Solving for the constants
- The Wronskian
- Worked example: the three cases confirmed
- Worked example: a variable coefficient pair
- A pair that fails
- Fundamental sets always exist
- Common mistakes to avoid
- Key takeaways
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