Journal
APPLIED MATHEMATICS AND COMPUTATION
Volume 218, Issue 22, Pages 10974-10981Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2012.04.058
Keywords
Riccati equation; Integrability condition; Applications in mechanics
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A new integrability condition of the Riccati equation dy/dx = a(x) + b(x)y + c(x)y(2) is presented. By introducing an auxiliary equation depending on a generating function f(x), the general solution of the Riccati equation can be obtained if the coefficients a(x), b(x), c(x), and the function f(x) satisfy a particular constraint. The validity and reliability of the method are tested by obtaining the general solutions of some Riccati type differential equations. Some applications of the integrability conditions for the case of the damped harmonic oscillator with time dependent frequency, and for solitonic wave, are briefly discussed. (C) 2012 Elsevier Inc. All rights reserved.
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