Method of variation of parameters
Variation of parameters is a more general way of solving second-order, linear, non-homogenous differential equation; i.e. of the form
Variation of parameters concerns the discovery of a particular solution, which can then be combined with the general solution of the complimentary homogenous equation. If the general solution is of the form
where
which are given by the Wronskian
This is in fact just an application of Cramer’s rule.
Generalisation to higher orders
A good explanation of the generalisation is given by this LibreText
Practice problems
- 2017. Elementary differential equations and boundary value problems, pp. 146–147 (§3.6 problems)