Riccati方程及其幂级数解法

Riccati differential equation and its power series solution

通过定理 2和定理 3,建立了 Riccati方程和二阶齐线性微分方程的关系 ,并利用二阶齐线性微分方程的幂级数解表示相应 Riccati方程的解 .

Normally,Riccati differential equation y′=p(x)y 2+Q(x)y+R(x) can not be solved by elementary method of integration.In this article,we set up the relation between Riccati differetial equation and second order homogeneows linear differential equation through theorem 1 and theorem 3,then we express the solution of Riccati differential equation by the power series solution of second order homogeneous linear differential equation.