Wronskian of functions or of a linear homogeneous ordinary differential equation
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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
ode::wronskian(Ly, y(x)) returns the wronskian
Ly defined as the element
where an -
1 is the coefficient of
degree n - 1 and n the
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
y(x)] which is a linear differential equation in
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
We can also compute the wronskian of
which is, up to a constant, the wronskian of
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
A homogeneous linear ordinary differential equation.
The dependent function of
A differential ring, default is