The paper investigates weak solutions of one-dimensional stochastic differential equations without drift but time-dependent coefficients. As in the preceding literature, this is done by means of an equivalent equation for time-changed Wiener processes. One-to-one relations between the equations regarding existence and uniqueness are presented. A new existence theorem is proved by monotone approximation of pure solutions. Furthermore, extreme solutions are investigated, turning out as pure in general and interesting for the problem of uniqueness in law.