The Cauchy problem for certain degenerated hyperbolic equation of third order (Q1902785)

We find the general solution to the equation \((\zeta+ \eta- \xi) u_{\xi \eta \zeta}+ \beta u_{\xi\zeta}- \alpha u_{\eta \zeta}=0\), \(0< \alpha, \beta<1\), \(\alpha+ \beta< 1\) in the domain \(G=\{ (\xi, \eta, \zeta)\mid \eta+ \zeta- \xi> 0\}\) of a three-dimensional Euclidean space and to a certain Cauchy problem for this equation.