摘要
文章利用待定函数法,把二阶变系数线性齐次微分方程降阶为一阶线性齐次微分方程,由此得出二阶变系数线性齐次微分方程y″+p(x)y′+q(x)y=0具有特解■的充要条件为■,并给出此类微分方程的一个通解形式,以及应用举例.
In this paper,the second order homogeneous linear differential equations with variable coefficients y″+p(x)y′+q(x)y=0 are reduced to the first order homogeneous linear differential equations by using the method of undetermined function.Thus,the sufficient and necessary conditionλ[p2(x)/(1-λ)2+p′(x)/1-λ]+q(x)=0 is given out for second order homogeneous linear differential equation with variable coefficients y″+p(x)y′+q(x)y=0 existing a special solution as the form y=e^λ/1-λ∫p(x)dx(λ≠0,1).Then,the general solutions of the equation are obtained.Examples are also provided for illustrating the applications.
作者
张云
叶永升
ZHANG Yun;YE Yongsheng(School of Mathematical Sciences,Huaibei Normal University,235000,Huaibei,Anhui,China)
出处
《淮北师范大学学报（自然科学版）》
CAS
2019年第1期86-88,共3页
Journal of Huaibei Normal University：Natural Sciences
基金
安徽省省级质量工程项目:精品开放课程(2017kfk042)
大规模在线开放课程(MOOC)示范项目(2015mooc053)
教学研究项目(2016jyxm0932
2017jyxm0216
2017jyxm0214)
教学团队(2015jxtd120)
淮北师范大学教学研究项目(jy2017105
jy2017111
jy2017127)
关键词
变系数
线性
微分方程
特解
variable coefficient
linear
differential equation
special solution
