For a fourth-order equation with two independent variables a variant of the Goursat problem with data on two intersecting characteristics is considered. It includes not only the construction of the desired function, but also the coefficients of the equation. Thus, we are talking about the inverse problem of determining the coefficients of the equation. The method of construction of conditions providing allocation of infinite number of sets of this type equations is offered, for which the

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... under consideration is solvable in quadratures. Instead of introducing additional boundary conditions, restrictions on the structure of the equation are proposed, related to the possibilities of its factorization.