Canonical equation (1) has oscillating solutions, if the coefficient a(x) is positive and the function meets the Lipschitz condition. We have determined the solutions of this equation by sequence iteration method and directly proved that they are oscillating. However, in this work we have shown that the equation (1) has oscillating solutions even when the coefficient a(x) is small, when and integral diverges with a(x) which can be, but it does not have to be monotonous. If a(x) is not monotonous function, then all intervals of monotony of the coefficient a(x) should be determined. Then in each of these intervals the number and locations of zero oscillations should be also determined.
