The Cauchy problem for the hyperbolic differential equation of the third order

In the article the Cauchy problem for the third order hyperbolic differential equation with nonmultiple characteristics is considered on the plane of two independent variables. The differential equation has tree nonmultiple characteristics and this equation is strongly hyperbolic equation. The regular solution of the Cauchy problem for the hyperbolic differential equation of the third order with the nonmultiple characteristics is constructed in an explicit form, the solution is obtained by the method of general solutions. The solution of the Cauchy problem enables describing the propagation of initial displacement, initial velocity and initial acceleration.