Solving the Cauchy and Boundary Value Problem for a Continuous Multiplicative Differential Equation of the Second Order

Abstract

In the presented work, the Cauchy and boundary value problem for the inhomogeneous equation with the second order multiplicative derivative in the case of discontinuity is considered. The general solution of the considered equation, which depends on two arbitrary constants, has been obtained. Then, when looking at the Cauchy problem, these arbitrary constants are determined from the given initial conditions, and when looking at the boundary problem, these arbitrary constants are determined from the given boundary conditions. Thus, analytical expressions have been obtained for the solution of the problems considered both in the Cauchy problem and in the boundary problem. Moreover, in the continuous case, an analytical expression has been obtained for the solution of the Cauchy and boundary problem considered for the second formulation multiplicative derivative inhomogeneous differential equation. Thus, all seven algebraic operations and integration operations are involved in this analytical expression.