⑩天掌 Teaching Plan on Advanced Mathematics o 用常数变易法把C换成n,即令 y=l(x+1) 则 =u(x+1)2+2(x+1) d x 代入所给非齐次方程得 u=(x+1)2即a=2(x+1)2+C 故所得方程的通解为 y=(x+1)22(x+1)2+C tianjin polytechnic dmivendityTianjin Polytechnic University Teaching Plan on Advanced Mathematics 用常数变易法,把C换成u,即令2 y = u(x +1) 则 ( 1) 2 ( 1) 2 = u  x + + u x + dx dy 代入所给非齐次方程,得 2 1 u  = (x + 1) 即 u = x + 2 + C 3 ( 1) 3 2 故所得方程的通解为       y = x + x + 2 + C 3 2 ( 1) 3 2 ( 1)