A computation related to the link between a second order linear differential equation and a Ricatti equation gives a solution to a Schwartz differential equation

= | 2Q(z) |
(314) |

where

= | (315) |

Suppose that *y*_{1} and *y*_{2} are two solutions of the second order equation

y'' + 2Q(z) |
= | 0 | (316) |

whose nonvanishing and linear indepencence is established by their having a unit Wronskian,

= | 1. | (317) |

Starting with the definition

w(z) |
= | (318) |

there follow

w'(z) |
= | [y_{2}(z)]^{-2}, |
(319) |

= | (320) | ||

= | (321) | ||

= | (322) |

according to which such a quotient solves the equation. The involvement of the Ricatti equation arises from concluding that the only other solutions of the Schwartz equation result from a change of basis from the two solutions