xy - sin(πy²) = 0 x = 0 时,y = ±1
y + xy' - 2πyy'cos(πy²) = 0 (1)
y'[x - 2πy cos(πy²)] = -y
y' = y/ [x - 2πy cos(πy²)]
y'(0) = -1/(-2π) = 0.5
对(1)再求一次导数,解出:y''
代入x=0,y=-1,y‘(0)=0.5 就可以得到:y''(0)的值了.
xy - sin(πy²) = 0 x = 0 时,y = ±1
y + xy' - 2πyy'cos(πy²) = 0 (1)
y'[x - 2πy cos(πy²)] = -y
y' = y/ [x - 2πy cos(πy²)]
y'(0) = -1/(-2π) = 0.5
对(1)再求一次导数,解出:y''
代入x=0,y=-1,y‘(0)=0.5 就可以得到:y''(0)的值了.