Question

求助怎么解微分方程y" － sin y = x ，求这个微分方程的通解

Answer 1

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 (积分)
==>tan(x-y)+sec(x-y)=x+C (C是任意常数)

追问

可答案不是这个啊

求助