Journal of Pure and Applied Mathematics: Advances and ApplicationsAuthor'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.
