Author's: TIBERIU HARKO, FRANCISCO S. N. LOBO and M. K. MAK
Pages: [115] - [129]
Received Date: May 16, 2013
Submitted by:
Using Euler’s theorem on the integrability of the general
anharmonic oscillator equation [1], we present three distinct classes
of general solutions of the highly nonlinear second order ordinary
differential equation The first exact solution is obtained from a
particular solution of the point transformed equation
which is equivalent to the anharmonic
oscillator equation, if the coefficients
satisfy an integrability condition. The
integrability condition can be formulated as a Riccati equation for
and
respectively. By reducing the integrability
condition to a Bernoulli type equation, two exact classes of solutions
of the anharmonic oscillator equation are obtained.
anharmonic oscillations, integrability conditions, exact solutions.