d9b0a162-82a3-48cf-b4c9-f7600603964a20230828071050441wseas:wseasmdt@crossref.orgMDT DepositEQUATIONS2732-99762944-914610.37394/232021https://wseas.com/journals/equations/41220234122023310.37394/232021.2023.3https://wseas.com/journals/equations/2023.phpFedor EgorovichLomovtsevMechanics and Mathematics Faculty Belarusian State University Minsk, BELARUSA correction method of test solutions into classical solutions to a new inhomogeneous model wave equation with variable two-rates in the first quarter of the plane was developed to derive the minimum smoothness requirement of its right-hand side. In the case of different rates, it is not possible to derive the minimum smoothness of right-hand side of the inhomogeneous model wave equation in the first quarter of the plane without correcting both test generalized and test classical solutions. In this paper, classical solutions to the inhomogeneous two-rate model wave equation and the smoothness criterion of their right-hand side are obtained. We need them to find explicit unique and stable classical solutions and Hadamard correctness criteria to mixed (initial-boundary) problems for this wave equation using developed by the author of the ”implicit characteristics method”.8282023828202341435https://wseas.com/journals/equations/2023/a10equations-003(2023).pdf10.37394/232021.2023.3.5https://wseas.com/journals/equations/2023/a10equations-003(2023).pdfF.E. Lomovtsev, “Correction method of test solutions to the general wave equation in the first quarter of the plane for the minimum smoothness of its right-hand side,“ Zhurnal Belorussky state university. Mathematics. Computer science. No. 3. pp.38–52. 2017. F.E. Lomovtsev, “In the curvilinear first quarter of the plane, the correction method of test solutions for the minimum smoothness of the righthand side of the wave equation with constant coefficients,“ Kulyashov. No. 2 (60). Seryya B. Pryrodaznauchyya sciences (mathematics, physics, biology). pp.