Differential Equations › Section D · Laplace transforms › Topic D.5
Solving initial value problems
Here the Laplace transform earns its keep: transform the equation, solve an algebra problem for the unknown transform, and invert. The initial conditions enter at the first step, so the answer arrives with every constant already fixed.
In this topic
- Back to differential equations
- Derivatives of any order
- The method in three steps
- Worked example: a first order problem
- Worked example: a damped oscillator
- Worked example: forcing from rest
- How it compares with earlier methods
- Initial conditions away from zero
- Transfer functions and poles
- Common mistakes to avoid
- Key takeaways
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