On the plane, we consider a linear partial differential equation of arbitrary order of hyperbolic type. The operator in the equation is a composition of first-order differential operators. The equation is accompanied with Cauchy conditions. For the equation, we obtain an analytic form of the general solution, from which we single out the unique classical solution of the Cauchy problem.

We consider the Cauchy problem for a nonstrictly hyperbolic equation of arbitrary order with constant coefficients. The operator in the equation is a composition of first-order differential operators. The equation is supplemented with Initial conditions. We find the solution of this problem on a half-plane in analytic form in the case of two independent variables under some conditions on the coefficients.

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