<p>We introduce a new class of quantum stochastic differential equations, which will be called quantum stochastic Tricomi equation. We give general solutions as quantum stochastic processes, using the Wick product and linear combinations of annihilation operator and creation operator. For a particular case, these solutions are functions of momentum operator and position operator which are two algebraic (non-commuting) random variables with gaussian distribution. As application, the attractivity and the stability of these solutions are studied, using an adequate space of holomorphic generalized functions, the symbol map, and new notions of quantum white noise stability.</p>