苏州市职业大学学报
囌州市職業大學學報
소주시직업대학학보
JOURNAL OF SUZHOU VOCATIONAL UNIVERSITY
2014年
3期
49-52
,共4页
二阶常系数线性微分方程%降阶法%特征根%一阶微分形式
二階常繫數線性微分方程%降階法%特徵根%一階微分形式
이계상계수선성미분방정%강계법%특정근%일계미분형식
two order linear differential equation with constant coefficients%depression of order%characteristic root%first-order differential form
考虑二阶常系数线性微分方程的降阶法。首先，写出二阶齐次常系数线性微分方程的特征方程，求出特征方程的两个特征根；然后，利用积分因子乘以微分方程和导数的运算，将二阶常系数线性微分方程化为一阶微分形式；最后，将一阶微分形式两边同时积分，求解一阶线性微分方程，可求得二阶常系数线性微分方程的一个特解或通解。利用降阶法，可以求得微分方程的一个特解或通解。其计算方法简单和方便，在实际中具有应用价值。
攷慮二階常繫數線性微分方程的降階法。首先，寫齣二階齊次常繫數線性微分方程的特徵方程，求齣特徵方程的兩箇特徵根；然後，利用積分因子乘以微分方程和導數的運算，將二階常繫數線性微分方程化為一階微分形式；最後，將一階微分形式兩邊同時積分，求解一階線性微分方程，可求得二階常繫數線性微分方程的一箇特解或通解。利用降階法，可以求得微分方程的一箇特解或通解。其計算方法簡單和方便，在實際中具有應用價值。
고필이계상계수선성미분방정적강계법。수선，사출이계제차상계수선성미분방정적특정방정，구출특정방정적량개특정근；연후，이용적분인자승이미분방정화도수적운산，장이계상계수선성미분방정화위일계미분형식；최후，장일계미분형식량변동시적분，구해일계선성미분방정，가구득이계상계수선성미분방정적일개특해혹통해。이용강계법，가이구득미분방정적일개특해혹통해。기계산방법간단화방편，재실제중구유응용개치。
Depression of order for two order linear differential equation with constant coefficients is considered. First of all,the characteristic equation of linear differential equation with constant coefficients is written,and two characteristic roots are obtained,and then the differential equation is multiplied by the integral factor and operatied with derivative,the two order linear differential equation with constant coefficients is changed into the first-order differential form,and finally the first-order differential form is integrated.The two order linear differential equation becomes the linear differential equation of first order,solving first-order linear differential equations,and special or general solution of the differential equations can be obtained.The method is simple, convenient and very useful in practice.
