Differential Equations › Section E · Systems of differential equations › Topic E.3
Solutions to systems
A clever guess turns the homogeneous system x′ = Ax into an eigenvalue problem. This topic makes that guess, shows when a handful of solutions is enough to build every solution, and uses the Wronskian to check.
In this topic
- A guess borrowed from one equation
- Worked example: two exponential solutions
- Checking a solution directly
- Superposition
- Fundamental sets and the Wronskian
- Worked example: a fundamental set and an initial value
- Why a non-zero Wronskian matters
- The link to second-order equations
- Three cases ahead
- Common mistakes to avoid
- Key takeaways
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