2.解非齐次方程 dy+P(x)y=Q(x) d 用常数变易法：作变换)=(x)e∫P()dx则 WePp(eP(x)e Q() 即 (dir. 两端积分得 u=JQ(x)ePdx+C 故原方程的通解 y=ere[dx+c 即 y-Cee)dx 齐次方程通解 非齐次方程特解对应齐次方程通解 P x x y Ce − ( )d = 齐次方程通解 非齐次方程特解  − P x x Ce ( )d 2. 解非齐次方程 ( ) ( ) d d P x y Q x x y + = 用常数变易法: ( ) ( ) , − ( )d = P x x y x u x e 则  −  P x x u e ( )d + P(x)  − P x x u e ( )d = Q(x) 故原方程的通解 e Q x e x P x x P x x ( ) d ( )d ( )d    − + ( )d ( )d ( ) d P x x P x x y e Q x e x C −     = +      即 y = 即 作变换  − − P x x P x u e ( )d ( ) u Q x e x C P x x = +   ( ) d ( )d 两端积分得