解：∵y"=sin(x-y)

==>dy/dx=sin(x-y)

==>1-(1-dy/dx)=sin(x-y)

==>1-d(x-y)/dx=sin(x-y)

==>d(x-y)/dx=1-sin(x-y)

==>d(x-y)/(1-sin(x-y))=dx

==>(1+sin(x-y))d(x-y)/((1-sin(x-y))(1+sin(x-y)))=dx

(等式左端分子分母同乘(1+sin(x-y)))

==>(1+sin(x-y))d(x-y)/((1-sin(x-y))(1+sin(x-y)))=dx

==>(1+sin(x-y))d(x-y)/(1-(sin(x-y))^2)=dx

==>(1+sin(x-y))d(x-y)/(cos(x-y))^2=dx

==>((sec(x-y))^2+sec(x-y)tan(x-y))d(x-y)=dx

==>∫((sec(x-y))^2+sec(x-y)tan(x-y))d(x-y)=∫dx (積分)

==>tan(x-y)+sec(x-y)=x+C (C是任意常數)

∴此方程的通解是tan(x-y)+sec(x-y)=x+C。