1恰当方程的定义 定义1若有函数(x,y),使得 ault y)=M(x, y)dx+N(x, y)dj 则称微分方程 M(, y)dx+N(, y)dy=0, (1) 是恰当方程.此时(1)的通解为n(x,y)=C 如d(xy)=xy+yx=0 d(x'y+xy)=(3xy+y)dx+(x+2xy)dy=0 ddf(xdx+g(y)dy)=f(r) dx+g()dy=0 是恰当方程定义1 若有函数u(x, y),使得 du(x, y) = M (x, y)dx + N(x, y)dy 则称微分方程 M (x, y)dx + N(x, y)dy = 0, (1) 是恰当方程. 此时(1)的通解为u(x, y) = c. 如 xdy + ydx = 0 (3 ) ( 2 ) 0 2 2 3 x y + y dx + x + x y dy = f (x)dx + g( y)dy = 0 是恰当方程. d(xy) = ( + ) = 3 2 d x y x y+ =   d( f (x)dx g( y)d y) 1 恰当方程的定义