We study a modified Cauchy problem for the degenerate hyperbolic equation of the second kind. First, we find the representations of the general solution of the analyzed equation for α ≤ 1. Then, by using these representations, we formulate modified Cauchy problems for all real values of α and deduce the formulas for the solution of the analyzed problems. Further, it is shown that the obtained solutions indeed satisfy the investigated equation and the initial conditions.

中文翻译：

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一类退化双曲方程的修正柯西问题

我们研究了第二类退化双曲方程的修正柯西问题。首先，我们找到 α ≤ 1 时所分析方程的通解的表示。然后，通过使用这些表示，我们为 α 的所有实数值制定修正的柯西问题，并推导出所分析问题的解的公式。此外，它表明所获得的解决方案确实满足所研究的方程和初始条件。