2. dx xsin(xy)x 解令z=x,则 dz =y+r d dz xsin(xy)x sinz 分离变量法得2z-sin2z=4x+C, 将z=x代回, 所求通解为2x-sin(2xy)=4x+C; sin ( ) 1 2. 2 x y dx x xy dy = − 解 , dx dy y x dx dz 则 = + , sin 1 ) sin ( ) 1 ( 2 2 x z y x xy y x dx dz = + − = 分离变量法得 2z − sin2z = 4x + C, 将 z = xy 代回, 所求通解为 2xy − sin(2xy) = 4x +C. 令 z = xy