8.10. The Relation Between The Homogeneous And
be a linear differential operator of order n.
solution of the homogeneous equation
. Let y1
be a particular solution of the nonhomogeneous equation
. Then the general solution for
be any solution of
. Since L
is linear, we have
Thus, Theorem 8.10 breaks down the problem of solving a
nonhomogeneous equation into 2 parts.
One is to find a particular solution, the other is to solve the
homogeneous equation. This has a simple
geometric analogy: to find all points on a plane, we find a particular point on
the plane, then add to it all points on the parallel plane that goes through