Summary: Variation of Constants?
Let us recall how we solved
(IVP).
dy
dx
+ p(x)y(x) = q(x), y(x0) = y0
First solve
dµ
dx
+ p(x)y(x) = 0, µ(x0) = 1.
(This µ is the reciprocal of the one we considered earlier, but it fits the current context better as we shall
see.) We calculate
d
dx
µ(x)-1
y(x) = -µ(x)-2 dµ
dx
y(x) + µ(x)-1 dy
dx
= -µ(x)-2

Source: Allard, William K. - Department of Mathematics, Duke University

Collections: Mathematics