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The authors suggest setting up a modified Cauchy problem for one of the spatial analogues of the EulerDarboux equation with the data on the coefficient singularity line. Problem C1 was solved by the Riemann method. Problems C2 and C3 were solved by constructing a general solution of the equation in question whose formula provided the solutions to the problems.doi:10.24412/9215-0365-2021-63-3-52-61 fatcat:kwdbdp6zlrchpntjt35t4gtomu