Tests if a homogeneous linear ordinary differential equation is of Fuchsian type
This functionality does not run in MATLAB.
ode::isFuchsian(Ly
, y(x
), <AllExponents>)
ode::isFuchsian
returns TRUE
if Ly
is
of Fuchsian type, i.e., all the singular points (including the point
at infinity) of Ly
are regular. It returns FALSE
if
at least one singular point is irregular. When the option AllExponents
is
given, either FALSE
is returned or a list where each element is a table containing, at each regular singular
point of Ly
the place, the indicial equation and
the exponents.
We test if the following differential equation is Fuchsian:
Ly:=x*(1x)*diff(y(x),x$2)+(1x)*diff(y(x),x)+10*y(x)
ode::isFuchsian(Ly, y(x))
We can have a look of the indicial equations, exponents at each
regular singular point of Ly
:
ode::isFuchsian(Ly, y(x), AllExponents)
In this example, the Airy equation, the only singular point is at infinity and is irregular:
ode::isFuchsian(diff(y(x),x$2)x*y(x), y(x))

A homogeneous linear ordinary differential equation with coefficients in the field ℚ(x) of rational functions over the rationals. 

The dependent function of 

Return a list of tables of indical equations and exponents for regular singular points. 