The master equations of density operators describing the single-mode cavity driven by an oscillating external field in diffusion process can be concisely solved by th e thermo entangled state representation and the technique of integration within an ordere d product of operators.Based on the corresponding relation between the real mode operators an d fictitious mode operators acting on the thermo entangled state,the master equations of density operator can be converted into the evolution equation of the state vector,and the forma l solution can be easily obtained.Further,we deduce the analytical evolution formula for the density op erator in the infinitive Klaus operator-sum representation in this model.In addition,two mu tually Hermite conjugate Klaus operators are proved to satisfy the normalization condition.As an application of Klaus operator-sum solution,we investigate the evolutions of an initial coherent state and an initial vacuum state in this model.The results show that the coherent state a nd the vacuum state both evolve to thermal fields.