We shall investigate the Feynman approximation for the solutions of Cauchy problem for special type of differentional equations of second order of a branching manifold Y3. These solutions will be represented as a limit of multiple integrals over Cartesian powers of configuration space, as multiplicity tends to infinity. Such representations are called a Lagrangian Feynman formulae. We consider the collection of differentional equations which can describe the diffusion or similar processes on a branching manifold Y3, which can be described as a Cartesian multiplication of a real line R and a graph consisting of one vertex and 3 rays. The coefficients of heat conductivity are considered to be the parameters of our equations. And their solutions satisfy natural border conditions - the consistence of functions on common line of Y3 and the analogue of Kirchhoffâ€™s circuit law (the sum of derivatives of the solution taken with coefficients, equals 0). These conditions specify the Feynman formula which is used to solve the problem.