n阶常系数非齐次线性微分方程的降阶解法

The Method of Order Reducing for the General Solution of Order n Non-homogeneous Linear Differential Equation with Constant Coefficients

给出一阶线性非齐次微分方程的积分因子解法,避免了常数变易法带来的不便和不自然;给出n阶常系数非齐次线性微分方程的降阶解法,可以看出,高阶常系数线性非齐次微分方程最终都可以归结为求解一阶线性微分方程,从而避免了待定系数法求非齐次方程特解的繁琐,并最终说明了一般微积分教材中只给出两种类型常系数非齐次线性微分方程的待定系数解法的原因.

We present integrating factor method of first-order linear differential equation, which is the avoidance of the inconvenient and unnatural methods of variation of constant. Give the method of order reducing for the general solution of order n non-homogeneous linear differential equation with constant coefficients, which implies that, to find solution of high order non-homogeneous linear differential equation with constant coefficients are at last to solve first-order linear differential equation, and is avoid the complicated of the method of undetermined coefficient. Lastly, we explain why there are only two common kinds of non-homogeneous linear differential equations with constant coefficients by the method of undetermined coefficients.