⑩天掌 Teaching Plan on Advanced Mathematics o 有两个相等的实根(△ 特征根为r=r1=-P,-特解为y=en, 设另一特解为y2=l(x)e4, 将y2,y2,y代入原方程并化简, u+(2r+p)+(r2+pr1+q)=0, 知"=0,取(x)=x,则y2=xenx, 得齐次方程的通解为y=(C1+C2x)e; tianjin polytechnic dmivendityTianjin Polytechnic University Teaching Plan on Advanced Mathematics 有两个相等的实根 , 1 1 r x , y = e 2 1 2 p r = r = − ( = 0) 一特解为 得齐次方程的通解为 ( ) ; 1 1 2 r x y = C + C x e 将 y2 ，y2  ，y2  代入原方程并化简， (2 ) ( ) 0, 1 2 u + r1 + p u + r1 + pr + q u = 知 u = 0, 取 u(x) = x, , 1 2 r x 则 y = xe ( ) , 1 2 r x 设另一特解为 y = u x e 特征根为