Differential Equations › Section B · First order differential equations › Topic B.1
Linear equations and integrating factors
Every first-order linear equation can be solved by the same short procedure: multiply by one well-chosen function and the equation collapses into a single derivative. This topic makes that procedure routine and shows what the solution formula reveals about long-term behaviour.
In this topic
- Where linear equations fit
- The integrating factor
- Worked example: a polynomial forcing term
- Worked example: a variable coefficient
- Transient and steady state
- Worked example: behaviour that depends on y(0)
- When the integral cannot be done
- Reading the method as a checklist
- Common mistakes to avoid
- Key takeaways
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