解2整理得(x+x2+y)+(1+x)y=0 aP 00 ,∴是全微分方程 ay A用曲线积分法: (x,y)=(x2+x3+y)x+d B凑微分法: dy+(xdy+ ydx)+x dx+xdx=0, 4 x dy+d(xy)+d+d=0, 3 d(y+xy+ )=0.解2 整理得 ( ) (1 ) 0, 2 3 x + x + y dx + + x dy = 1 , x Q y P   = =    是全微分方程. A 用曲线积分法: ( , ) ( ) , 0 0 2 3   = + + + x y u x y x x y dx dy B 凑微分法: ( ) 0, 2 3 dy + xdy + ydx + x dx + x dx = 0， 3 4 ( ) 3 4 + + + = x d x dy d xy d ) 0. 3 4 ( 3 4 + + + = x x d y xy