“Riccati Differential Equation”的概念、定义、习题解题方法及翻译-数学辞典

单词

Riccati Differential Equation

释义

Riccati Differential Equation

(1)

where

. The transformation

(2)

leads to the second-order linear homogeneous equation

(3)

Another equation sometimes called the Riccati differential equation is

(4)

which has solutions

(5)

Yet another form of ``the'' Riccati differential equation is

(6)

which is solvable by algebraic, exponential, and logarithmic functions only when

, for

,1, 2, ....

References

Abramowitz, M. and Stegun, C. A. (Eds.). ``Riccati-Bessel Functions.'' §10.3 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 445, 1972.

Glaisher, J. W. L. ``On Riccati's Equation.'' Quart. J. Pure Appl. Math. 11, 267-273, 1871.

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