反之着y=(x)为35舶的连续解则有 0(x)=y+f(,9()t 由于f(x,y)在R上连续,从而f(t,0()连续, 故对上式两边求导,得 do(x) f(x,p(x)) x 且(x)=y+f(x,(x)x=y 即y=0(x)为(3.1)的连续解反之 若y =(x)为(3.5)的连续解,则有 x y f t t dt x x = + 0 ( ) ( , ( ))  0  由于f (x, y)在R上连续, 从而f (t,(t))连续, 故对上式两边求导,得 ( , ( )) ( ) f x x dx d x   = 且 0 0 0 0 0 (x ) y f (x, (x))dx y x x = + =    即y =(x)为(3.1)的连续解