In this paper the initial value problem and global properties of solutions are studied for the scalar second order ODE: (vertical bar u'vertical bar(l)u')' + c vertical bar u'vertical bar(alpha)u' + d vertical bar u vertical bar(beta)u = 0, where alpha, beta, l, c, d are positive constants. In particular, existence, uniqueness and regularity as well as optimal decay rates of solutions to 0 are obtained depending on the various parameters, and the oscillatory or non-oscillatory behavior is elucidated.