On the solution of a class of the reduced wave equation and the Riccati differential equation

In this paper we present an “iteration” technique for a class of differential equation having the form z″=λzz″=λz, where λλ is a function in C∞C∞. We show that we can construct not only the general solution of the reduced wave equation but also the general solution of the Riccati differential equation by using this iteration technique if the given function λλ is satisfies the conditionλ2n-1λ2n-2=λ2n-3λ2n-4≔β.Then we give a simple application of this technique to inverse conductive scattering problem for an inhomogeneous spherical medium.