Calculus › Section G · Differential equations › Topic G.5
First-order linear equations
Separation solves equations that factor neatly; many useful ones do not. First-order linear equations, the kind behind mixing tanks and circuits, always yield to one trick: multiply by the right factor and the left side collapses into a single derivative.
In this topic
- The form this method needs
- The integrating factor
- Worked example: y′ + 3y = e²ˣ
- Worked example: variable coefficients
- Particular plus homogeneous
- Worked example: a filling tank
- An RL circuit
- Linear, separable, or both?
- Why linear equations are dependable
- Common mistakes to avoid
- Key takeaways
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Standards: Beyond AP