Mathematics · University
Initial-value problems and equilibrium · revision notes
Solving a differential equation produces constants; initial conditions select a particular solution.
Key ideas and conditions
General versus particular
Solving a differential equation produces constants; initial conditions select a particular solution.
Equilibrium
A constant solution is found by setting the derivative to zero.
Existence and uniqueness
Conditions on the right-hand side matter; continuity alone does not always imply uniqueness.
Verification
Differentiate a proposed solution and check both the equation and the initial condition.
Explain without looking
- Which form is the homogeneous part of y′+ay=b for a>0?
- Explain why dividing by y when solving y′=y can hide a solution.
Further reading and review references
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