Transforms a linear differential system to an equivalent scalar linear differential equation
This functionality does not run in MATLAB.
ode::scalarEquation(A
, x
, y
, <Transform>)
ode::scalarEquation
converts a first order
homogeneous linear differential system to an equivalent homogeneous
scalar linear differential equation using the method of cyclic vector.
ode::scalarEquation(A, x, y)
returns a scalar
homogeneous linear differential equation in y(x)
equivalent
to the first order homogeneous differential system
using the
method of the cyclic vector. If the option Transform
is
given then a list is returned whose first element is the corresponding
differential equation Ly
and second element is
an invertible matrix P
such that
is
the companion matrix associated to Ly
; hence if Z
is
a solution of the differential system
then PZ is
a solution of the system
.
We compute a linear differential equation equivalent to the following differential system:
A := matrix( [ [x^21,1,0], [0,x^2+5*x+1/3,1], [0,0,2]])
l := ode::scalarEquation(A, x, y, Transform)
And we can check that, for P=l[2]
,
is
the companion matrix associated to l[1]
:
P := l[2]: bool( diff(P,x)*P^(1)+P*A*P^(1) = ode::companionSystem(l[1], y(x)) )

A square matrix of type 

The independent variable of the resulting scalar differential equation. 

The dependent variable of the resulting scalar differential equation. 
Expression or a list.