Description of Method
Given an ordinary non-homogeneous linear differential equation of order n
- (i)
let be a fundamental system of solutions of the corresponding homogeneous equation
- (ii)
Then a particular solution to the non-homogeneous equation is given by
- (iii)
where the are continuous functions which satisfy the equations
- (iv)
By substituting (iii) into (i) and applying (iv) it follows that
- (v)
The linear system (v) of n equations can then be solved using Cramer's rule yielding
where is the Wronskian determinant of the fundamental system and is the Wronskian determinant of the fundamental system with the i-th column replaced by
The particular solution to the non-homogeneous equation can then be written as
Read more about this topic: Variation Of Parameters
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