摘要
利用特解讨论了二阶变系数齐次线性微分方程,得到了形如y=y*{c1∫(y*)-2 exp[-∫p(x)d x]dx+c 2}的通解公式,同时,利用常数变易法得到了非齐次方程的通解,改进和推广了相关文献中的结论。
A second order linear differential equation with variable coefficient has been studied, and a general solution is given by use of the special solution, as follows y=y^*{c1∫(y^*)^-2exp[-∫p(x)dx]dx+c2}. Meanwhile, the general solution of inhomogeneous equation is given by use of the method of variation of constant. Some recent results in relative articles are extended and improved.
出处
《新乡学院学报》
2011年第4期301-302,共2页
Journal of Xinxiang University
关键词
通解
特解
二阶线性变系数微分方程
general solution
special solution
second order linear differential equations with variable coefficient