Let P denote the class of functions p(z) that are analytic in the unit disk E and satisfy the conditions \(p(0)=1\) and Re p(z)\(>0\) for \(z\in E\). Let \[ S(w,\alpha)=w(z)+\alpha zw'(z)/w(z), \] where \(\alpha >0\) and w(z) is analytic in E with w(z)\(\neq 0\) and \(w(0)=1\). The author proves that, if \(\lambda\) (\(\alpha)\) is a positive, nondecreasing function satisfying a certain other condition, then the solution q(z) (if it exists) of the equation \[ \exp \int^{b}_{a}\ln S(q,\alpha)d\lambda (\alpha)=p(z) \] (p(z)\(\in P)\) also belongs to P.