「例1求解x2y"+x=1 「解特点是:不显含y 令y=p=p(x) x p+ xp=l p+-p P +-Inlx 2 →y=xx +Inx积分得通解 y=CIn(x+In2 x+C2 2021/2/202021/2/20 5 [ 1] 1 2 例 求 解 x y + xy = [解] 特点是：不显含 y 令 y = p = p(x) 1 2 x p + xp = 2 1 1 x p x p + = x x x C p ln 1 1 = + x x x C y ln 1 1  = + 积分,得通解 2 2 1 ln 2 1 y = C ln x + x + C