例1求=x+y2满足y1l=0的特解 解xn=0 设y=a1x+a2x2+a3x3+…+anx"+…, y=a1+2a2x+303x2+…+nanx+ 将y,y的幂级数展开式带入原方程 a1+2a2x+33x2+44xC°+ =x+(1x+a2x2+a3x+a4x+| 0 . 0 求 = x + y 2 满足y x= = 的特解 dx dy 解  x 0 = 0 ， 0 , y 0 = , 3 3 2 设 y = a1 x + a2 x + a x ++ an x n + 将 y, y的幂级数展开式带入原方程 a1 + 2a2 x + 3a3 x2 + 4a4 x3 +4 2 4 3 3 2 1 2 = x + (a x + a x + a x + a x +) 2 3 , 2 1 3 1 y = a1 + a2 x + a x ++ nan xn− + 例 1