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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