The second-order linear differential equation (p(x)y′)′ + q(x)y = 0; x 2 (0; T] is considered, It is shown that the recti able oscillations near x = 0 of solu- tions are characterized by the integrability of q1=4p􀀀3=4 on (0; T). The fractal dimension of bounded oscillatory solutions is also calculated.