Forward and inverse problems with discontinuous coefficient

We consider an almost linear differential equation with discontinuous coefficient with respect to the derivative on time. The Cauchy problem is stated and investigated. The inverse problem is stated after studding differential properties of a generalized solution for the forward problem. In the inverse problem we look for a line where the coefficients are discontinuous is sought for. Additionally, the solution of the forward problem is given on a certain plane outside the line. The main result of the article is an algorithm for solving the inverse problem. This investigation may be treated as a part of the theory of probing heterogeneous media by physical signals.