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^2-1,1,0], [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, is the companion matrix associated to l:
P := l: bool( diff(P,x)*P^(-1)+P*A*P^(-1) = ode::companionSystem(l, y(x)) )
A square matrix of type Dom::Matrix.
The independent variable of the resulting scalar differential equation.
The dependent variable of the resulting scalar differential equation.