高数-微分方程-高阶常系数非齐次线性方程的特解.pdf

高等数学——微分方程高阶常系数非齐次线性方程的特解2010年8月~10月解读《2010版考研数学复习指南（理工类,文登考研培训特供版）》P160,表6-6------------------------------------------------------------------------------------------------------------------------1.原方程为ynPyn1Pyn2PyPyekx............................................................112n1n1.1.k是FD0的m重根，nm0...............................................................................11.2.原方程为ypyqyekx...............................................................................................62.微分算子对三角函数的若干性质..............................................................................................72.1.正弦函数............................................................................................................................72.2.余弦函数............................................................................................................................72.3.正弦函数+余弦函数..........................................................................................................8nn1n23.原方程为yPyPyPyPysinx......................................................812n1n3.1.i是FD0的m重根，km0...........................................................................83.2.i不是FD0的根..................................................................................................20nn14.原方程为yPyPyPyekxhx..................................................................271n1n4.1.微分算子法的结论..........................................................................................................284.2.位移定理FDekxuxekxFDkux...................................................................28nn15.原方程为yPyPyPyvx，其中vx为关于x的m阶多项式..........291n1n5.1.对于幂函数的微积分用排列数统一表示......................................................................295.2.待定系数法，0不是特征根，即P0........................................................................29n5.3.微分算子法，0不是特征根，即P0...........................................................