We consider the solvability results and two efficient approximation methods for the solution of a two space dimensional coefficient inverse problem for a transport-like equation which is related to an integral geometry problem for a general curve class. The main difficulty of this study is the overdeterminacy of the problem which is achieved by replacing the overdetermined inverse problem with a determined one by using some extension of the class of unknown functions. Investigation of the approximate solution of the problem is considered by using an analytical approximation and finite difference method.