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factoring out a singularity of a 2nd order ordinary differential equation

ODE textbook with links to Complex analysis2nd order ordinary differential equation problemSecond order differential equation, orthogonalityIdentifying Types of Singularity in Differential EquationsPolar 2nd Order Ordinary Differential EquationSeries solutions to differential equations: singularities in equation and solution?2nd order ordinary differential equation and solutionsAlgorithm for solving a large class of linear 2nd order ODEs with polynomial coefficients.Solving linear ordinary, 2nd order differential equations via global integral bases.linear differential equation with two regular, one irregular singular point

1

$begingroup$

I am looking at a 2nd order ODE:

beginequation
fracd^2udx^2 + p(x)fracdudx + q(x) u = 0 .
endequation

that has five regular singular points: say at $0$, $1$, $a$, $b$, and $infty$, where $a$ and $b$ are real numbers. I suspect I can ``factor out'' one singularity of the equation (as is done for example for another equation here), and thus transform this equation into a Heun equation. Is there a general way/theory/procedure to determine when one can factor out a singularity for a given ode? I'd greatly appreciate a simple demonstration, example, or references to the literature on this subject.

ordinary-differential-equations reference-request singularity

share|cite|improve this question

edited Apr 1 at 19:11

Ernie060

2,940719

asked Apr 1 at 17:51

JustinJustin

85

$endgroup$

add a comment | 

1

$begingroup$

I am looking at a 2nd order ODE:

beginequation
fracd^2udx^2 + p(x)fracdudx + q(x) u = 0 .
endequation

that has five regular singular points: say at $0$, $1$, $a$, $b$, and $infty$, where $a$ and $b$ are real numbers. I suspect I can ``factor out'' one singularity of the equation (as is done for example for another equation here), and thus transform this equation into a Heun equation. Is there a general way/theory/procedure to determine when one can factor out a singularity for a given ode? I'd greatly appreciate a simple demonstration, example, or references to the literature on this subject.

ordinary-differential-equations reference-request singularity

share|cite|improve this question

edited Apr 1 at 19:11

Ernie060

2,940719

asked Apr 1 at 17:51

JustinJustin

85

$endgroup$

add a comment | 

$begingroup$

I am looking at a 2nd order ODE:

beginequation
fracd^2udx^2 + p(x)fracdudx + q(x) u = 0 .
endequation

that has five regular singular points: say at $0$, $1$, $a$, $b$, and $infty$, where $a$ and $b$ are real numbers. I suspect I can ``factor out'' one singularity of the equation (as is done for example for another equation here), and thus transform this equation into a Heun equation. Is there a general way/theory/procedure to determine when one can factor out a singularity for a given ode? I'd greatly appreciate a simple demonstration, example, or references to the literature on this subject.

ordinary-differential-equations reference-request singularity

share|cite|improve this question

edited Apr 1 at 19:11

Ernie060

2,940719

asked Apr 1 at 17:51

JustinJustin

85

$endgroup$

share|cite|improve this question

edited Apr 1 at 19:11

Ernie060

2,940719

asked Apr 1 at 17:51

JustinJustin

85

share|cite|improve this question

edited Apr 1 at 19:11

Ernie060

2,940719

asked Apr 1 at 17:51

JustinJustin

85

edited Apr 1 at 19:11

Ernie060

2,940719

edited Apr 1 at 19:11

Ernie060

2,940719

asked Apr 1 at 17:51

JustinJustin

85

asked Apr 1 at 17:51

JustinJustin

85