| 可积的Riccati微分方程的不变量变换讨论 |
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| 引用本文： | 赵临龙.可积的Riccati微分方程的不变量变换讨论[J].数学的实践与认识,2008,38(16). |
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| 作者姓名： | 赵临龙 |
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| 作者单位： | 陕西安康学院数学系,陕西,安康,725000 |
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| 基金项目： | 陕西省精品课程建设项目，陕西省教育厅教学研究项目 |
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| 摘 要： | 对于可积的Riccati微分方程:Ly]=-y′+p(x)yn+Q(x)y+R(x)(p(x)R(x)≠0,n≠0,1)(0)Ly]=-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Ly0]=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Ly0]≠0,讨论其可积性.
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| 关 键 词： | Riccati方程 解 不变量变换 |
A Study on Invariant Transform of Riccati Differatial Equation |
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| ZHAO Lin-long.A Study on Invariant Transform of Riccati Differatial Equation[J].Mathematics in Practice and Theory,2008,38(16). |
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| Authors: | ZHAO Lin-long |
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| Abstract: | It is to educe the sufficient conditions of integrability for the integrable Riccati differential equations:Ly]=-y′+p(x)yn+Q(x)y+R(x)(p(x)R(x)≠0,n≠0,1)(0)Ly]=-y′+p(x)y2+Q(x)y+R(x)(p(x)R(x)≠0)(1)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). |
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| Keywords: | riccati equation solution invarant transformation |
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