一类广义Riccati方程的三个可积判据

Three Integrable Criterions of One Kind of Generalized Riccati Equation

考虑一类广义Riccati方程,通过函数变换,在所给条件下,将这类方程等价地化为变量分离方程,从而得到了该方程可积的三个充分性判据,并给出方程通解的参数表达形式,扩大了Riccati方程的可解性范围.

This paper considers one kind of generalized Riccati equation. Changing the equation to variable separate equation equal in value with the definite conditions by transformation of function, acquires three efficient integrable criterions of the equation, and gives the parameter form of its general solution. Expand the extent of the equation that can be solved.