∵[A(y)]²+xsin[πA(y)]+2x-3=0,且A(y)可微
==>2A(y)A'(y)y'+sin[πA(y)]+πxA'(y)y'cos[πA(y)]+2=0 (等式两端对x求导数)
==>[2A(y)+πxcos[πA(y)]]A'(y)y'=-2-sin[πA(y)]
∴y'=-[2+sin[πA(y)]/{[2A(y)+πxcos[πA(y)]]A'(y)}
∵A(0)=A'(0)=1
∴dy/dx|(y=0)=y'|(y=0)
=-[2+sin[πA(0)]/{[2A(0)+πxcos[πA(0)]]A'(0)}
=-[2+sin(π)/[2+πxcos(π)]
=-2/(2-πx)
=2/(πx-2).