I'm a little confused with ODEs. After two weeks of trying to figure out Frobenius I have finally realized that there seems to be two different power set used by all of my three books for the y substitution but I am unsure when to use either one. Here are the two sets that i'm talking about:(adsbygoogle = window.adsbygoogle || []).push({});

Set 1 from section 6.1

[tex] y = \sum_{n=0}^\infty C_n x^n [/tex]

[tex] y\prime = \sum_{n=1}^\infty n C_n x^{n-1}[/tex]

[tex] y\prime\prime = \sum_{n=2}^\infty n(n-1) C_n x^{n-2}[/tex]

set 2 from section 6.2

[tex] y = \sum_{n=0}^\infty n C_n x^{n-1} [/tex]

[tex] y\prime = \sum_{n=0}^\infty n C_n x^{n-1} [/tex]

[tex] y\prime\prime = \sum_{n=0}^\infty n(n-1) C_n x^{n-2} [/tex]

I think I have come to understand that I should use set 1 if and only if all of the singular points are irregular and set 2 when I have at least one regular singular point. Is this correct? If not, when is it appropriate to use set 1 rather than set 2? Or is set 2 only designed to work with Frobenius' method while set 1 only works lacking a Taylor power series expansion?

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Frobenius Method

Loading...

Similar Threads for Frobenius Method | Date |
---|---|

I Solution of an ODE in series Frobenius method | Dec 23, 2016 |

Quick question about method of Frobenius | Jan 12, 2016 |

Frobenius method for fourth order linear ODE | Dec 18, 2013 |

Solve Legendre Polynomial using Method of Frobenius | Oct 3, 2013 |

Frobenius Method - Roots differ by integer | Jul 11, 2012 |

**Physics Forums - The Fusion of Science and Community**