Unimodular transformation of a linear ordinary differential equation
This functionality does not run in MATLAB.
ode::unimodular(Ly, y(x), <Transform>)
ode::unimodular(Ly, y(x)) tests if the linear homogeneous differential equation Ly has a unimodular Galois group (i.e. the wronskian lies in the base field ℚ(x)), if not transforms Ly into a unimodular one (by changing the second highest coefficient to zero) and returns a table with index equation and factorOfTransformation containing respectively the transformed differential equation and the factor of transformation Wn such that a solution of the transformed equation multiplied by Wn is a solution of Ly.
If the option Transform is given then Ly is transformed unconditionally even if Ly has yet a unimodular Galois group.
We test if the following differential equation has a unimodular Galois group:
Ly := y(x)*6+x*diff(y(x),x)*(-2)+diff(y(x),x$2)*(-x^2+1)
It is unimodular since the factor of transformation is 1. We can also check this by computing the wronskian of Ly which is a rational function:
Now we transform Ly into a differential equation whose wronskian is 1:
ode::unimodular(Ly, y(x), Transform)
A homogeneous linear differential equation over ℚ(x).
The dependent function of Ly.