Wronskian of functions or of a linear homogeneous ordinary differential equation
This functionality does not run in MATLAB.
ode::wronskian(l, x, <R>) ode::wronskian(Ly, y(x), <R>)
ode::wronskian computes the wronskian (determinant) of functions or of a linear homogeneous ordinary differential equation.
ode::wronskian(l, x) returns the wronskian, i.e. the determinant of the wronskian matrix, of the elements of l with respect to x.
ode::wronskian(Ly, y(x)) returns the wronskian of Ly defined as the element w such that , where an - 1 is the coefficient of Ly of degree n - 1 and n the order of Ly.
If the optional argument R is given, then the specified differential ring will be chosen for representing the entries of the wronskian matrix.
We compute the wronskian of [2*x^2+1, x*sqrt(1+x^2), y(x)] which is a linear differential equation in y(x):
Ly:=ode::wronskian([2*x^2+1, x*sqrt(1+x^2), y(x)], x)
Ly := numer( normal(Ly) )
And we can check that a basis of solutions of Ly is as expected:
We can also compute the wronskian of Ly, which is, up to a constant, the wronskian of x^2+1 and x*sqrt(x^2+1):
ode::wronskian(Ly, y(x)), simplify(ode::wronskian([x^2+1/2,x*sqrt(1+x^2)], x))
A list of functions of the variable x.
A homogeneous linear ordinary differential equation.
The dependent function of Ly.
A differential ring, default is Dom::ExpressionField(id, iszero@normal).