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DEtools[regularsp] - compute the regular singular points of a second order non-autonomous linear ODE
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Calling Sequence
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regularsp(des, ivar, dvar)
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Parameters
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des
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second order linear ordinary differential equation or its list form
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ivar
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indicates the independent variable when des is a list with the ODE coefficients
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dvar
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indicates the dependent variable, required only when des is an ODE and the dependent variable is not obvious
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Description
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Important: The regularsp command has been deprecated. Use the superseding command DEtools[singularities], which computes both the regular and irregular singular points, instead.
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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
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p(x) y''(x) + q(x) y'(x) + r(x) y(x) = 0, p(x) <> 0, p'(x) <> 0
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a point alpha is considered to be a regular singular point if
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1) alpha is a singular point,
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2) limit( (x-alpha)*q(x)/p(x), x=alpha ) = 0 and
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limit( (x-alpha)^2*r(x)/p(x), x=alpha ) = 0.
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The results are returned in a list. In the event that no regular singular points are found, an empty list is returned.
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Examples
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Important: The regularsp command has been deprecated. Use the superseding command DEtools[singularities], which computes both the regular and irregular singular points, instead.
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An ordinary differential equation (ODE)
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Warning, DEtools[regularsp] has been superseded by DEtools[singularities]
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![[0, 1]](/support/helpjp/helpview.aspx?si=9586/file07209/math151.png)
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The coefficient list form
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![coefs := [21*(x^2-x+1), 0, 100*x^2*(x-1)^2]](/support/helpjp/helpview.aspx?si=9586/file07209/math164.png)
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![[0, 1, infinity]](/support/helpjp/helpview.aspx?si=9586/file07209/math171.png)
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You can convert convert an ODE to the coefficient list form using DEtools[convertAlg] form
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![L := [[1/x+x, 5*x-x^2, 2*x^2+5*x^3], 0]](/support/helpjp/helpview.aspx?si=9586/file07209/math197.png)
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![[-2/5, infinity]](/support/helpjp/helpview.aspx?si=9586/file07209/math204.png)
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| (9) |
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