摘要
对于可积的Riccati微分方程:L[y]=-y′+p(x)yn+Q(x)y+R(x)(p(x)R(x)≠0,n≠0,1)(0)L[y]=-y′+p(x)y2+Q(x)y+R(x)(p(x)R(x)≠0)(1)利用其不变量变换,给出方程(0)和(1)的可积充分条件,并对方程(1)的特解形式L[y0]=0,讨论其不变量变换的等效性;同时,对方程(1)的非特解形式L[y0]≠0,讨论其可积性.
It is to educe the sufficient conditions of integrability for the integrable Riccati differential equations :
L[y]=-y'+p(x)y^n+Q(x)y+R(x) (p(x)R(x)≠0,n≠0.1)
L[y]=-y'+p(x)y^n+Q(x)y+R(x) (p(x)R(x)≠0)
by using of their invariants, is to discuss the equal effects of invarants transformation to the parxicular solution (1), while is to discuss the integrability of non-particular solution to the equation (1).
出处
《数学的实践与认识》
CSCD
北大核心
2008年第16期205-209,共5页
Mathematics in Practice and Theory
基金
陕西省精品课程建设项目(2005-80)
陕西省教育厅教学研究资助项目(04G32)