homogeneous linear differential equation
The linear differential equation
(1) |
is called
homogeneous (http://planetmath.org/HomogeneousLinearDifferentialEquation)
iff . If ,
the equation (1) is inhomogeneous.
If (1) is homogeneous (http://planetmath.org/HomogeneousLinearDifferentialEquation),
then the sum of any solutions is a solution and any solution
multiplied by a constant is a solution.
The special case
of (1), where the ’s are constants, can via the
substitution be transformed into a homogeneous
linear differential equation of the same order but with
constant coefficients.
Title | homogeneous linear differential equation |
---|---|
Canonical name | HomogeneousLinearDifferentialEquation |
Date of creation | 2014-02-27 10:07:04 |
Last modified on | 2014-02-27 10:07:04 |
Owner | pahio (2872) |
Last modified by | pahio (2872) |
Numerical id | 3 |
Author | pahio (2872) |
Entry type | Definition |
Classification | msc 34A05 |