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
Famous quotes containing the words description of, description and/or method:
“To give an accurate description of what has never occurred is not merely the proper occupation of the historian, but the inalienable privilege of any man of parts and culture.”
—Oscar Wilde (1854–1900)
“The great object in life is Sensation—to feel that we exist, even though in pain; it is this “craving void” which drives us to gaming, to battle, to travel, to intemperate but keenly felt pursuits of every description whose principal attraction is the agitation inseparable from their accomplishment.”
—George Gordon Noel Byron (1788–1824)
“Letters are above all useful as a means of expressing the ideal self; and no other method of communication is quite so good for this purpose.... In letters we can reform without practice, beg without humiliation, snip and shape embarrassing experiences to the measure of our own desires....”
—Elizabeth Hardwick (b. 1916)