方程xy-sin(派y^2)=0确定y是x的函数,求Y''(X=0,Y=-1)二阶导数

Question

方程xy-sin(派y^2)=0确定y是x的函数,求Y''(X=0,Y=-1)二阶导数

Answer 1

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.