Differential Equations › Section B · First order differential equations › Topic B.6
Existence, uniqueness, and intervals of validity
Before solving an equation it pays to know whether a solution exists, whether it is the only one, and how far it reaches. Two theorems answer these questions, and they reveal a deep difference between linear and nonlinear equations.
In this topic
- Questions to ask before solving
- The linear theorem
- Worked example: an interval without solving
- The nonlinear theorem
- Worked example: losing uniqueness
- Worked example: an interval that depends on y(0)
- Linear and nonlinear compared
- Uniqueness keeps solutions apart
- Common mistakes to avoid
- Key takeaways
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