关于三阶线性微分方程的一个求解公式

General Solution for Third-order LDE

对于3阶非齐次线性微分方程y′′′+py″+qy′+ry=f,由它对应齐次方程的2个线性无关特解y1,y2与其Wronski行列式w,应用降阶法推导出一个求解公式为y=y1(C3+∫w/y12(C2+∫y1/w2e-∫pdx(C1+∫w2y12fe∫pdxdx)dx)dx).

For the differential equation y″＋py″＋qy′＋ry=f,assuming Yl, Y2 are two linearly independent particular solutions and w is the corresponding Wronskian determinant, we derive the following formula for the general solution of the differential equation by using the order reduction method. y=y1（C3＋∫ ω/y1^2（C2＋∫ y1/ω2 e-∫pdx（C1＋∫ ω2/y1^2 ∫ w2/yi^2 fe ∫pdx dx）dx）dx）.