故对应齐次方程通解为y=c(x+1) p(xdx x+1 y=ce - ce =c(x+1) 其次应用常数变易法求非齐线性方程的通解, 令y=c(x)(x+1)"为原方程的通解代入得 dc(x) x+1)+nc(x)(x+1n=n(x)(x+1)-+e(x+1) x dc(x) =e积分得c(x)=e+c dx 故通解为y=(x+1)(ex+c,c为任意常数故对应齐次方程通解为 n y = c(x +1) 其次应用常数变易法求非齐线性方程的通解, 令y = c(x)(x +1) n 为原方程的通解,代入得 n n n x n x nc x x nc x x e x dx dc x ( 1) ( )( 1) ( )( 1) ( 1) ( ) 1 1 + + + = + + + − − 即 x e dx dc x = ( ) 积分得 ~ c(x) e c x = + 故通解为 为任意常数 ~ ~ y (x 1) (e c), c n x = + + n d x x n p x d x y ce ce c(x 1) 1 ( ) = +  =  = +