On a Singular Kamke Equation Equivalent to Linear Harmonic Oscillator

This paper investigates analytical properties of a singular Kamke second order equation consisting of a generalization of Kamke equation 6.110 and Kamke equation 6.111. It is shown that this equation belongs to the class of quadratic Lienard type equations closely related to the linear harmonic oscillator and introduced recently by some authors of this work. In this way, exact Kamke solutions are recovered. The connection between this equations and the linear harmonic oscillator shows its possible use in mechanical vibrations study and quantum mechanics.