homogeneous linear differential equation

The linear differential equation

an(x)y(n)+an-1(x)y(n-1)++a1(x)y+a0(x)y=b(x) (1)

is called homogeneousPlanetmathPlanetmath (http://planetmath.org/HomogeneousLinearDifferentialEquation) iff  b(x)0.  If  b(x)0, 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

cnxny(n)+cn-1xn-1y(n-1)++c1xy+c0y= 0

of (1), where the ci’s are constants, can via the substitution  x=et  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