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)
ODE ≔ ⅆ2ⅆx2⁢y⁡x=αx−1+βx+gammax2+δx−12+λ2⁢y⁡x
Warning, DEtools[regularsp] has been superseded by DEtools[singularities]
The coefficient list form
coefs ≔ 21⁢x2−x+1,0,100⁢x2⁢x−12:
You can convert convert an ODE to the coefficient list form using DEtools[convertAlg] form
ODE ≔ 2⁢x2+5⁢x3⁢ⅆ2ⅆx2⁢y⁡x+5⁢x−x2⁢ⅆⅆx⁢y⁡x+1x+x⁢y⁡x=0
L ≔ convertAlg⁡ODE,y⁡x
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