代入非齐方程 c'(x)(x+1)2+2c(x)(x+1) 1+I(x+1)2 2c(x)(x+1)2 →c'(x)=(x+1)2 解得c(x)=(x+1)2+c 3 故非齐次方程的通解为 y=(x+1)2(x+1)2+cl代入非齐方程 ( )( 1) 2 ( )( 1) 2 c x x + + c x x + 2 5 2 ( 1) 1 1 2 ( )( 1) = + + − +  x x c x x 2 1  c(x) = (x + 1) 解得 c x = x + + c 2 3 ( 1) 3 2 ( ) 故非齐次方程的通解为 ( 1) ] 3 2 ( 1) [ 2 3 2 y = x + x + + c