Method for solving differential equations with coefficients in the form of the Heaviside step function

The article deals with the method for solving differential equations and coefficients contain the Heaviside step function. As in an example, the solution of the firs order differential equation, which is the answer to the problem of momentless thermoelasticity on the surface under normal load is found.For the composition we obtain a generalized radius-vector, components of the metric tensor, and principal curvatures. The system of differential equations for T11, T22, and T12 is reduced to a first order differential equation for T11 with coefficients as Heaviside functions. An analytical solution of the system is obtained and graphs of T11 and T22 efforts are constructed.