compute the regular singular points of a second order non-autonomous linear ODE
regularsp(des, ivar, dvar)
second order linear ordinary differential equation or its list form
indicates the independent variable when des is a list with the ODE coefficients
indicates the dependent variable, required only when des is an ODE and the dependent variable is not obvious
Important: The regularsp command has been deprecated. Use the superseding command DEtools[singularities], which computes both the regular and irregular singular points, instead.
The regularsp command determines the regular singular points of a given second order linear ordinary differential equation. The ODE could be given as a standard differential equation or as a list with the ODE coefficients (see DEtools[convertAlg]). Given a linear ODE of the form
p(x) y''(x) + q(x) y'(x) + r(x) y(x) = 0, p(x) <> 0, p'(x) <> 0
a point alpha is considered to be a regular singular point if
1) alpha is a singular point,
2) limit( (x-alpha)*q(x)/p(x), x=alpha ) = 0 and
limit( (x-alpha)^2*r(x)/p(x), x=alpha ) = 0.
The results are returned in a list. In the event that no regular singular points are found, an empty list is returned.
An ordinary differential equation (ODE)
The coefficient list form
You can convert convert an ODE to the coefficient list form using DEtools[convertAlg] form
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